Finite Group Databasebeta

← #21455432

Subgroups — #21455432

Order 7808.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D61C211yesmaximal, characteristic, complemented
2#16840269C211yesmaximal, characteristic, complemented
3C2×#14519748C211yesmaximal, characteristic, complemented
4#16840012C212yesmaximal, complemented
5#16840005C212yesmaximal, complemented
6#16839995C212yesmaximal, complemented
7#16839988C212yesmaximal, complemented
8#16839804C211yesmaximal, characteristic, complemented
9#16839767C211yesmaximal, characteristic, complemented
10#16839763C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61—21no—
13C22×C4×D61C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758189C2212yescomplemented
16M16×D61—24no—
17C2×C8×D61C2212yescomplemented
18#14519758—21no—
19#14519753C2211yescharacteristic, complemented
20#14519753C2211yescharacteristic, complemented
21#14519748—21no—
22#14519748—21no—
23#14519748C2212yes—
24#14519748C2212yes—
25#14519748C2211yescharacteristic, complemented
26#14519748C2211yescharacteristic, complemented
27#14519745—21no—
28C4×C22⋊D61—21no—
29C4×C22⋊D61—21no—
30#14519736C2211yescharacteristic
31C2×C4⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61—21no—
33#14519711C2212yescomplemented
34#14519709C2212yescomplemented
35#14519701C2212yescomplemented
36#14519698C2212yescomplemented
37#14519698C2212yescomplemented
38#14519698C2212yescomplemented
39C2×#41×C61C2211yescharacteristic
40C22×D4×C61C2211yescharacteristic
41AGL(1,ℤ/8)×C61—24no—
42C2×SD16×C61C2212yescomplemented
43C2×D8×C61C2212yescomplemented
44C2×M16×C61C2211yescharacteristic
45C24×C61—21no—
46C23×D61D411yescharacteristic
47#41×C61—22no—
48#41×C61—22no—
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61—22no—
52C2×D4×C61—21no—
53C2×D4×C61—22no—
54C2×D4×C61C2311yescharacteristic
55C2×D4×C61C2312yes—
56C22×C4×C61—21no—
57C22×C4×C61C2311yescharacteristic
58C2×C22⋊D61—22no—
59C2×C22⋊D61—22no—
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—44no—
63C22×Dic61—21no—
64C22×Dic61D411yescharacteristic
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D411yescharacteristic
68C2×C4×D61D411yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×C4×D61C2311yescharacteristic
71SD16×C61—24no—
72D8×C61—24no—
73M16×C61D414yescomplemented
74C2×C8×C61C2312yes—
75C22⋊Dic61—21no—
76C22⋊Dic61—22no—
77C22⋊Dic61—22no—
78C22⋊Dic61—21no—
79C22⋊Dic61—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61C2311yescharacteristic
84C4⋊Dic61C2311yescharacteristic
85C4⋊Dic61C2312yes—
86#11758196—21no—
87#11758196—21no—
88C4×Dic61—21no—
89#11758194—22no—
90C2×#92418C2312yes—
91#11758189—24no—
92C8×D61—24no—
93C23×C61—21no—
94C23×C61—22no—
95C23×C61—42no—
96C23×C61—42no—
97C23×C61—42no—
98C23×C61C2×D411yescharacteristic
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—41no—
102C22×D61C2×D411yescharacteristic
103C22×D61C2×D411yescharacteristic
104Q8×C61—21no—
105Q8×C61—21no—
106D4×C61—21no—
107D4×C61—22no—
108D4×C61—22no—
109D4×C61—21no—
110D4×C61—42no—
111D4×C61—42no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D412yes—
116C2×C4×C61#4112yes—
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—42no—
119C22⋊D61—44no—
120C22⋊D61—42no—
121C22⋊D61—44no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—42no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C4×D61—22no—
130C4×D61—22no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C8×C61C2×D414yescomplemented
136#92418—22no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—41no—
140C22×C61—42no—
141C22×C61—42no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—42no—
145C22×C61—84no—
146C22×C61#12112yes—
147C22×C61C22×D411yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—44no—
154C2×D61AGL(1,ℤ/8)12yescomplemented
155C4×C61—41no—
156C4×C61#12112yes—
157C4×C61C22×D411yescharacteristic
158C4×C61C2×#4111yescharacteristic
159Dic61—21no—
160Dic61—21no—
161Dic61—42no—
162Dic61—41no—
163Dic61—41no—
164#3055—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61—81no—
167C2×C61—82no—
168C2×C61C2×#12111yescharacteristic
169C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C61#57511yescharacteristic
171D61—22no—
172D61—41no—
173C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
174C22×M16—611no—
175#525—611no—
176C2×#121—611no—
177#469—612no—
178#468—612no—
179#466—612no—
180#465—612no—
181#428—611no—
182#418—611no—
183#417—611no—
184C61#305511yescharacteristic, complemented, Sylow
185C2×#41C2×D6111yescharacteristic
186C22×D4—1221no—
187C22×D4C2×D6111yescharacteristic
188C23×C4—611no—
189AGL(1,ℤ/8)—24no—
190C2×SD16C2×D6112yescomplemented
191C2×D8C2×D6112yescomplemented
192C2×M16—611no—
193C2×M16—612no—
194C2×M16—1224no—
195C2×M16C2×D6111yescharacteristic
196C22×C8—612no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—611no—
200#121—612no—
201#121—612no—
202#121—611no—
203#121—611no—
204#121—1221no—
205#121—1221no—
206#120—1221no—
207C4×D4—1221no—
208C4×D4—1221no—
209#117—611no—
210C2×C4⋊C4—611no—
211C2×C22⋊C4—1221no—
212#107—612no—
213#106—612no—
214#103—612no—
215#102—612no—
216#102—612no—
217#102—612no—
218C24—21no—
219C24—611no—
220#41—22no—
221#41—22no—
222C2×Q8C22×D6111yescharacteristic
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—1221no—
228C2×D4—1221no—
229C2×D4—1222no—
230C2×D4—1222no—
231C2×D4—2444no—
232C2×D4C22×D6111yescharacteristic
233C2×D4C22×D6112yes—
234C22×C4—21no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1221no—
243C22×C4C22×D6111yescharacteristic
244SD16—24no—
245D8—24no—
246M16—1222no—
247M16—1224no—
248M16C22⋊D6114yescomplemented
249C2×C8—612no—
250C2×C8—1224no—
251C2×C8C22×D6112yes—
252C4⋊C4—611no—
253C4⋊C4—611no—
254C4⋊C4—612no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1222no—
261C22⋊C4—1222no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—1221no—
266C23—21no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—611no—
272C23—611no—
273C23—1222no—
274C23—1222no—
275C23—2441no—
276C23D4×D6111yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—22no—
281D4—22no—
282D4—21no—
283D4—42no—
284D4—42no—
285D4—2442no—
286D4—2444no—
287D4—2442no—
288D4—2444no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—1222no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1222no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1222no—
303C2×C4—2442no—
304C2×C4D4×D6111yescharacteristic
305C2×C4#1175822412yes—
306C2×C4C2×C22⋊D6112yes—
307C2×C4C23×D6111yescharacteristic
308C8—1222no—
309C8C2×C22⋊D6114yescomplemented
310C22—21no—
311C22—21no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—84no—
319C22—612no—
320C22—1221no—
321C22—1221no—
322C22—1221no—
323C22—1221no—
324C22—1221no—
325C22—2444no—
326C22#1451974812yes—
327C22C2×D4×D6111yescharacteristic
328C4—41no—
329C4—1221no—
330C4—1221no—
331C4—2442no—
332C4—2441no—
333C4—2441no—
334C4#1451974812yes—
335C4C22×C22⋊D6111yescharacteristic
336C4C2×#1175822411yescharacteristic
337C2—22no—
338C2—82no—
339C2—81no—
340C2—1222no—
341C2—2441no—
342C2C2×#1451974811yescharacteristic
343C2AGL(1,ℤ/8)×D6111yescharacteristic
344C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×M16×D61C2semidirect
2. #16840269C2semidirect
3. C2×#14519748C2semidirect
4. #16840012C2semidirect
5. #16840005C2semidirect
6. #16839995C2semidirect
7. #16839988C2semidirect
8. #16839804C2semidirect
9. #16839767C2semidirect
10. #16839763C2semidirect
11. C2×AGL(1,ℤ/8)×C61C2semidirect
15. C2×#11758189C22semidirect
17. C2×C8×D61C22semidirect
19. #14519753C22semidirect
20. #14519753C22semidirect
25. #14519748C22semidirect
26. #14519748C22semidirect
33. #14519711C22semidirect
34. #14519709C22semidirect
35. #14519701C22semidirect
36. #14519698C22semidirect
37. #14519698C22semidirect
38. #14519698C22semidirect
42. C2×SD16×C61C22semidirect
43. C2×D8×C61C22semidirect
73. M16×C61D4semidirect
135. C8×C61C2×D4semidirect
154. C2×D61AGL(1,ℤ/8)semidirect
173. C2×AGL(1,ℤ/8)D61semidirect
184. C61#3055semidirect
190. C2×SD16C2×D61semidirect
191. C2×D8C2×D61semidirect
248. M16C22⋊D61semidirect
309. C8C2×C22⋊D61semidirect