Finite Group Databasebeta

← #21454673

Subgroups — #21454673

Order 7808.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D61C211yesmaximal, characteristic
2#16840238C211yesmaximal, characteristic, complemented
3#16840234C211yesmaximal, characteristic
4#16839865C211yesmaximal, characteristic, complemented
5#16839862C211yesmaximal, characteristic, complemented
6#16839860C211yesmaximal, characteristic, complemented
7#16839859C211yesmaximal, characteristic, complemented
8C4×#11758190C211yesmaximal, characteristic, complemented
9SD16×Dic61C211yesmaximal, characteristic, complemented
10#16839849C211yesmaximal, characteristic, complemented
11#16839797C211yesmaximal, characteristic, complemented
12#16839769C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic
14#16839716C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21SD16×D61C418yescomplemented
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic, complemented
25C4×Dic122—21no—
26C4×Dic122C2211yescharacteristic, complemented
27#14519742—21no—
28#14519742C2211yescharacteristic, complemented
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735—21no—
35#14519735C2211yescharacteristic
36#14519735C2211yescharacteristic
37#14519734—21no—
38#14519734C2211yescharacteristic
39C2×#11758198—21no—
40C22⋊C4×D61—21no—
41#14519710C2211yescharacteristic, complemented
42#14519710C2211yescharacteristic, complemented
43#14519709C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519700C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519688C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C8×Dic61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C4×C8×C61C2211yescharacteristic, complemented
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66Q8×D61—22no—
67Q8×D61C2×C414yescomplemented
68D4×D61—22no—
69D4×D61C2×C414yes—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77SD16×C61C2×C414yescomplemented
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87#11758201C2×C414yescomplemented
88#11758200C2×C414yescomplemented
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190C2×C414yescomplemented
111#11758189—22no—
112C8×D61C2×C414yescomplemented
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—24no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61C2×D411yescharacteristic
119Q8×C61—21no—
120Q8×C61C22×C412yes—
121D4×C61—21no—
122D4×C61C22×C412yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—81no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—24no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—81no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244C22×C412yes—
140C4×D61—24no—
141C4×D61—81no—
142C4×D61—81no—
143C4×D61C22×C412yes—
144C4×D61#4112yes—
145Dic122—21no—
146Dic122—24no—
147Dic122C22×C412yes—
148C8×C61—21no—
149C8×C61C22×C412yes—
150#92418—21no—
151#92418C22×C412yes—
152C22×C61—22no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C2×D61C4×D412yes—
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C23×C411yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61C4×D412yes—
176#2949—611nomaximal, Sylow
177C2×C61—42no—
178C2×C61C2×C4×D411yescharacteristic
179C2×C61#57711yescharacteristic
180C2×C61#57711yescharacteristic
181D61—22no—
182D61—42no—
183C22×SD16—611no—
184#519—611no—
185#518—611no—
186#440—611no—
187#440—611no—
188#440—611no—
189#440—611no—
190C4×SD16—611no—
191C4×SD16—611no—
192C4×SD16—611no—
193C4×SD16D6111yescharacteristic, complemented
194#427—611no—
195#419—611no—
196#418—611no—
197#405—611no—
198C61#294911yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C22×D4—611no—
201C2×SD16—611no—
202C2×SD16—611no—
203C2×SD16—618no—
204C2×SD16—611no—
205C2×SD16C2×D6111yescharacteristic
206C2×M16—611no—
207C22×C8—611no—
208C4×Q8—611no—
209C4×Q8—611no—
210C4×Q8—611no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213C4×Q8C2×D6111yescharacteristic, complemented
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—1221no—
218C4×D4—1221no—
219C4×D4C2×D6111yescharacteristic
220#117—611no—
221#117—611no—
222#117—611no—
223#117—1221no—
224#117—1221no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227#107—611no—
228#107—611no—
229#106—611no—
230#106C2×D6111yescharacteristic, complemented
231#103—611no—
232#103—611no—
233#103—611no—
234#103C2×D6111yescharacteristic, complemented
235#102—611no—
236#102—611no—
237#102—611no—
238#102C2×D6111yescharacteristic
239#97—611no—
240#97—611no—
241C4×C8—611no—
242C4×C8C2×D6111yescharacteristic, complemented
243C24—1221no—
244C2×Q8—614no—
245C2×Q8—611no—
246C2×Q8—1221no—
247C2×Q8—1222no—
248C2×Q8C22×D6111yescharacteristic
249C2×D4—614no—
250C2×D4—611no—
251C2×D4—1222no—
252C2×D4—1221no—
253C2×D4C22×D6111yescharacteristic
254C22×C4—21no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260SD16—614no—
261SD16—614no—
262SD16—614no—
263SD16C4×D6114yescomplemented
264M16—1222no—
265C2×C8—611no—
266C2×C8—614no—
267C2×C8—611no—
268C2×C8C22×D6111yescharacteristic
269C2×C8C22×D6111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C42—21no—
289C42—611no—
290C42—1221no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—21no—
297C23—611no—
298C23—1224no—
299C23—1221no—
300C23—4881no—
301C23—4881no—
302Q8—21no—
303Q8—612no—
304Q8—1224no—
305Q8—1221no—
306Q8C2×C4×D6112yes—
307D4—21no—
308D4—612no—
309D4—1224no—
310D4—1221no—
311D4C2×C4×D6112yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—611no—
317C2×C4—612no—
318C2×C4—612no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1224no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4D4×D6111yescharacteristic
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—21no—
332C8—612no—
333C8—1221no—
334C8C2×C4×D6112yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—612no—
339C22—1221no—
340C22—1221no—
341C22—1222no—
342C22—4884no—
343C22—2441no—
344C22—2441no—
345C22C2×D4×D6111yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—612no—
352C4—1222no—
353C4—1221no—
354C4—1221no—
355C4—2441no—
356C4—2441no—
357C4C22×C4×D6111yescharacteristic
358C4#41×D6111yescharacteristic
359C2—42no—
360C2—1222no—
361C2—2442no—
362C2C4×D4×D6111yescharacteristic
363C2#1684056811yescharacteristic
364C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#2949
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #16840238C2semidirect
4. #16839865C2semidirect
5. #16839862C2semidirect
6. #16839860C2semidirect
7. #16839859C2semidirect
8. C4×#11758190C2semidirect
9. SD16×Dic61C2semidirect
10. #16839849C2semidirect
11. #16839797C2semidirect
12. #16839769C2semidirect
14. #16839716C2semidirect
15. C4×SD16×C61C2semidirect
21. SD16×D61C4semidirect
24. Q8×Dic61C22semidirect
26. C4×Dic122C22semidirect
28. #14519742C22semidirect
41. #14519710C22semidirect
42. #14519710C22semidirect
43. #14519709C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519700C22semidirect
50. #14519688C22semidirect
51. #14519687C22semidirect
52. C8×Dic61C22semidirect
54. C4×Q8×C61C22semidirect
56. #106×C61C22semidirect
57. #103×C61C22semidirect
59. C4×C8×C61C22semidirect
67. Q8×D61C2×C4semidirect
77. SD16×C61C2×C4semidirect
87. #11758201C2×C4semidirect
88. #11758200C2×C4semidirect
110. #11758190C2×C4semidirect
112. C8×D61C2×C4semidirect
193. C4×SD16D61semidirect
198. C61#2949semidirect
213. C4×Q8C2×D61semidirect
230. #106C2×D61semidirect
234. #103C2×D61semidirect
242. C4×C8C2×D61semidirect
263. SD16C4×D61semidirect