Finite Group Databasebeta

← #21456617

Subgroups — #21456617

Order 7808.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519748C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic, complemented
3#16840081C211yesmaximal, characteristic, complemented
4#16840079C212yesmaximal, complemented
5#16840078C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16840012C212yesmaximal, complemented
8#16839896C211yesmaximal, characteristic, complemented
9#16839894C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#447C211yesmaximal, characteristic, complemented
12C22×C22⋊D61—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2211yescharacteristic, complemented
15C22×C4×D61C2211yescharacteristic
16C2×#11758199C2212yescomplemented
17C2×#11758189C2212yescomplemented
18#14519752C2211yescharacteristic, complemented
19#14519751C2211yescharacteristic
20#14519750—21no—
21#14519749—21no—
22#14519748—21no—
23#14519748—21no—
24#14519748C2212yes—
25#14519748C2211yescharacteristic, complemented
26#14519748C2212yescomplemented
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C4⋊C4×D61C2211yescharacteristic, complemented
29C2×C22⋊Dic61—21no—
30C22⋊C4×D61—21no—
31#14519709C2212yescomplemented
32#14519708C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic, complemented
37#14519689C2212yescomplemented
38C22×D4×C61C2211yescharacteristic, complemented
39C2×D8×C61C2212yescomplemented
40#121×C61C2211yescharacteristic
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic, complemented
43C24×C61—21no—
44C23×D61—21no—
45C23×D61D411yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—42no—
49C2×D4×C61C2311yescharacteristic
50C2×D4×C61C2312yes—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—21no—
57C2×C22⋊D61—44no—
58C22×Dic61—21no—
59C22×Dic61D411yescharacteristic
60D4×D61—42no—
61D4×D61—44no—
62C2×D244—21no—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—42no—
66C2×C4×D61D411yescharacteristic
67C2×C4×D61D411yescharacteristic
68C2×C4×D61C2311yescharacteristic
69C2×C4×D61C2311yescharacteristic
70D8×C61—42no—
71C2×C8×C61C2312yes—
72C4⋊C4×C61C2311yescharacteristic
73C22⋊C4×C61—21no—
74C22⋊Dic61—21no—
75C22⋊Dic61—22no—
76C22⋊Dic61—22no—
77#11758199—42no—
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61C2311yescharacteristic
82C4⋊Dic61C2312yes—
83#11758196—21no—
84C2×#92418C2312yes—
85#11758189—42no—
86C23×C61—22no—
87C23×C61—21no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61C2×D411yescharacteristic
92C22×D61—22no—
93C22×D61—22no—
94C22×D61—21no—
95C22×D61—41no—
96C22×D61—42no—
97C22×D61—42no—
98C22×D61—42no—
99C22×D61C2×D411yescharacteristic
100C22×D61C2×D411yescharacteristic
101D4×C61—22no—
102D4×C61—22no—
103D4×C61—22no—
104D4×C61—42no—
105D4×C61—42no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2411yescharacteristic
110C22⋊D61—42no—
111C22⋊D61—42no—
112C22⋊D61—44no—
113C22⋊D61—42no—
114C22⋊D61—44no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61C2×D411yescharacteristic
120C2×Dic61C2×D411yescharacteristic
121D244—22no—
122D244—42no—
123C4×D61—22no—
124C4×D61—22no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—42no—
128C8×C61—22no—
129#92418—22no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—42no—
138C22×C61—84no—
139C22×C61AGL(1,ℤ/8)12yes—
140C22×C61C22×D411yescharacteristic
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—44no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—84no—
151C2×D61AGL(1,ℤ/8)12yes—
152C4×C61—21no—
153C4×C61—41no—
154C4×C61H(5,𝔽2)12yes—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—42no—
159#3192—611nomaximal, Sylow
160C2×C61—22no—
161C2×C61—81no—
162C2×C61—82no—
163C2×C61#53411yescharacteristic
164C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
166D61—22no—
167D61—41no—
168D61—81no—
169C2×#121—611no—
170C2×#121—611no—
171#481—611no—
172#481—612no—
173#481—611no—
174#469—612no—
175#469—612no—
176#447—611no—
177#447—612no—
178#447D6111yescharacteristic, complemented
179#407—611no—
180C61#319211yescharacteristic, complemented, Sylow
181C22×D4—611no—
182C22×D4—1221no—
183C22×D4—1221no—
184C22×D4C2×D6111yescharacteristic, complemented
185C23×C4—611no—
186C2×D8—612no—
187C2×D8C2×D6112yescomplemented
188C2×M16—612no—
189#121—612no—
190#121—611no—
191#121—612no—
192#121—611no—
193#121—611no—
194#121—1221no—
195#121—1221no—
196#121—1221no—
197#121—1221no—
198#121C2×D6111yescharacteristic
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C22⋊C4—1221no—
202C2×C22⋊C4—1221no—
203#106—612no—
204#106—612no—
205#102—612no—
206#102—612no—
207#102—612no—
208#102C2×D6112yescomplemented
209C22⋊C8—611no—
210C22⋊C8—612no—
211C22⋊C8C2×D6111yescharacteristic, complemented
212C24—21no—
213C24—611no—
214C24—1221no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—611no—
219C2×D4—1221no—
220C2×D4—1221no—
221C2×D4—1222no—
222C2×D4—1221no—
223C2×D4—1222no—
224C2×D4—1221no—
225C2×D4—2442no—
226C2×D4—2444no—
227C2×D4—2444no—
228C2×D4C22×D6111yescharacteristic
229C2×D4C22×D6112yes—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—2442no—
238C22×C4C22×D6111yescharacteristic
239D8—42no—
240D8—2442no—
241M16—2442no—
242C2×C8—612no—
243C2×C8C22×D6112yes—
244C4⋊C4—611no—
245C4⋊C4—612no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4C22×D6111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—1221no—
251C22⋊C4—1221no—
252C22⋊C4—1222no—
253C22⋊C4—1222no—
254C22⋊C4—1221no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—611no—
261C23—611no—
262C23—1222no—
263C23—1222no—
264C23—1221no—
265C23—2441no—
266C23—2442no—
267C23—2442no—
268C23—2442no—
269C23D4×D6111yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—1222no—
276D4—2442no—
277D4—2442no—
278D4—2444no—
279D4—2444no—
280D4—2442no—
281D4—2442no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—1222no—
289C2×C4—1221no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2442no—
295C2×C4D4×D6111yescharacteristic
296C2×C4C23×D6111yescharacteristic
297C8—22no—
298C8—1222no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—612no—
309C22—1221no—
310C22—1221no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—4884no—
315C22—2444no—
316C22—2441no—
317C22—2441no—
318C22—2441no—
319C22#1451980112yes—
320C22C2×D4×D6111yescharacteristic
321C4—21no—
322C4—41no—
323C4—1221no—
324C4—1221no—
325C4—2442no—
326C4—2441no—
327C4#1451982212yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—1222no—
332C2—4881no—
333C2—2441no—
334C2#1684032211yescharacteristic
335C2AGL(1,ℤ/8)×D6111yescharacteristic
336C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3192
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#14519748C2semidirect
2. #121×D61C2semidirect
3. #16840081C2semidirect
4. #16840079C2semidirect
5. #16840078C2semidirect
6. #16840014C2semidirect
7. #16840012C2semidirect
8. #16839896C2semidirect
9. #16839894C2semidirect
10. #16839724C2semidirect
11. C61×#447C2semidirect
14. C2×D4×D61C22semidirect
16. C2×#11758199C22semidirect
17. C2×#11758189C22semidirect
18. #14519752C22semidirect
25. #14519748C22semidirect
26. #14519748C22semidirect
27. C2×C4⋊Dic61C22semidirect
28. C4⋊C4×D61C22semidirect
31. #14519709C22semidirect
32. #14519708C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519698C22semidirect
36. C22⋊#92418C22semidirect
37. #14519689C22semidirect
38. C22×D4×C61C22semidirect
39. C2×D8×C61C22semidirect
41. #102×C61C22semidirect
42. C22⋊C8×C61C22semidirect
178. #447D61semidirect
180. C61#3192semidirect
184. C22×D4C2×D61semidirect
187. C2×D8C2×D61semidirect
208. #102C2×D61semidirect
211. C22⋊C8C2×D61semidirect