Finite Group Databasebeta

← #21455362

Subgroups — #21455362

Order 7808.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519797C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic, complemented
3#16840245C211yesmaximal, characteristic, complemented
4#16839982C212yesmaximal, complemented
5#16839975C212yesmaximal, complemented
6#16839960C212yesmaximal, complemented
7#16839955C212yesmaximal, complemented
8#16839790C211yesmaximal, characteristic, complemented
9#16839764C211yesmaximal, characteristic, complemented
10C2×#14519698C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13#14519797—24no—
14C2×#11758202C2211yescharacteristic, complemented
15C2×#11758200C2211yescharacteristic, complemented
16C2×#11758201C2211yescharacteristic, complemented
17C2×#11758199C2211yescharacteristic, complemented
18C22×#92418C2211yescharacteristic
19#14519773C2212yes—
20#14519764C2212yes—
21#14519748—21no—
22#14519748—21no—
23#14519746—22no—
24Q8×Dic61C2212yescomplemented
25D4×Dic61—22no—
26D4×Dic61C2212yescomplemented
27#14519736—21no—
28#14519736C2211yescharacteristic
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2211yescharacteristic
31#14519706C2212yescomplemented
32#14519706C2212yescomplemented
33#14519702C2212yescomplemented
34#14519699C2212yescomplemented
35#14519698C2212yes—
36#14519698C2212yes—
37C2×#41×C61C2211yescharacteristic
38C22×D4×C61C2211yescharacteristic
39AGL(1,ℤ/8)×C61—24no—
40C2×SD16×C61C2212yes—
41C2×D8×C61C2212yes—
42C2×M16×C61C2211yescharacteristic
43C24×C61—21no—
44#41×C61—22no—
45#41×C61D414yescomplemented
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—21no—
48C2×D4×C61—22no—
49C2×D4×C61—21no—
50C2×D4×C61—22no—
51C2×D4×C61C2312yes—
52C2×D4×C61C2311yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61C2311yescharacteristic
55C2×C22⋊D61—21no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—22no—
58C22×Dic61—21no—
59C22×Dic61—22no—
60#11758222—22no—
61#11758222—22no—
62C2×D244C2311yescharacteristic
63C2×C4×D61—21no—
64C2×Dic122C2311yescharacteristic
65SD16×C61—24no—
66D8×C61—24no—
67M16×C61—22no—
68C2×C8×C61C2312yes—
69C22⋊Dic61—22no—
70C22⋊Dic61—22no—
71C22⋊Dic61—22no—
72C22⋊Dic61D412yes—
73#11758202—22no—
74#11758201—22no—
75#11758200—22no—
76#11758199—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61—22no—
79C4⋊Dic61D411yescharacteristic
80C4⋊Dic61D411yescharacteristic
81C4⋊Dic61C2312yes—
82C4×Dic61—22no—
83C4×Dic61C2312yes—
84C2×#92418—22no—
85C2×#92418C2311yescharacteristic
86C2×#92418C2311yescharacteristic
87C23×C61—21no—
88C23×C61—22no—
89C23×C61—42no—
90C23×C61—81no—
91C23×C61—81no—
92C23×C61C2×D411yescharacteristic
93C22×D61—21no—
94Q8×C61—21no—
95Q8×C61C2×D412yes—
96D4×C61—24no—
97D4×C61—22no—
98D4×C61—21no—
99D4×C61—22no—
100D4×C61—42no—
101D4×C61C2×D412yes—
102C2×C4×C61—21no—
103C2×C4×C61—24no—
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D412yes—
106C2×C4×C61#4112yes—
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—42no—
109C22⋊D61—82no—
110C22⋊D61—82no—
111C2×Dic61—22no—
112C2×Dic61—21no—
113C2×Dic61—82no—
114C2×Dic61—81no—
115C2×Dic61C2×D412yes—
116C2×Dic61C2×D412yes—
117D244—21no—
118D244—21no—
119C4×D61—42no—
120Dic122—21no—
121Dic122—21no—
122C8×C61—22no—
123#92418—21no—
124#92418—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—22no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61—42no—
133C22×C61—84no—
134C22×C61#12112yes—
135C22×C61C22×D411yescharacteristic
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C4×C61—22no—
140C4×C61#12112yes—
141C4×C61C22×D411yescharacteristic
142C4×C61C2×#4111yescharacteristic
143Dic61—22no—
144Dic61—22no—
145Dic61—41no—
146Dic61—42no—
147#3045—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61—42no—
150C2×C61—82no—
151C2×C61C2×#12111yescharacteristic
152C2×C61#57611yescharacteristic
153C2×C61#57711yescharacteristic
154D61—81no—
155C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
156C2×#135—611no—
157#535—611no—
158#520—611no—
159#464—612no—
160#463—612no—
161#460—612no—
162#459—612no—
163#424—611no—
164#417—611no—
165C2×#102—611no—
166C61#304511yescharacteristic, complemented, Sylow
167C2×#41—611no—
168C2×#41C2×D6111yescharacteristic
169C22×D4C2×D6111yescharacteristic
170AGL(1,ℤ/8)—24no—
171#135—1224no—
172C2×Q16—611no—
173C2×SD16—611no—
174C2×SD16—611no—
175C2×SD16C2×D6112yes—
176C2×D8—611no—
177C2×D8C2×D6112yes—
178C2×M16C2×D6111yescharacteristic
179C22×C8—611no—
180#127—612no—
181#124—612no—
182#121—1221no—
183#121—1221no—
184#120—1222no—
185C4×Q8—612no—
186C4×D4—612no—
187C4×D4—1222no—
188#117—611no—
189#117—1221no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C4⋊C8—612no—
193C4⋊C8—612no—
194#103—612no—
195#102—612no—
196#102—612no—
197#102—612no—
198C24—21no—
199#41—22no—
200#41—1222no—
201#41—1222no—
202#41C22⋊D6114yescomplemented
203C2×Q8—611no—
204C2×Q8C22×D6111yescharacteristic
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—611no—
210C2×D4—1222no—
211C2×D4—1222no—
212C2×D4—1221no—
213C2×D4C22×D6112yes—
214C2×D4C22×D6111yescharacteristic
215C22×C4—21no—
216C22×C4—1222no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C22×D6111yescharacteristic
220Q16—1222no—
221SD16—24no—
222SD16—1222no—
223SD16—1222no—
224D8—24no—
225D8—1222no—
226M16—22no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—1222no—
230C2×C8C22×D6112yes—
231C4⋊C4—611no—
232C4⋊C4—611no—
233C4⋊C4—612no—
234C4⋊C4—1222no—
235C4⋊C4—1221no—
236C22⋊C4—612no—
237C22⋊C4—1222no—
238C22⋊C4—1222no—
239C22⋊C4—1222no—
240C42—612no—
241C42—1222no—
242C23—21no—
243C23—22no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—1221no—
248C23D4×D6111yescharacteristic
249Q8—21no—
250Q8—1221no—
251Q8—1221no—
252Q8C2×C22⋊D6112yes—
253D4—24no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—1221no—
259D4—1221no—
260D4—4882no—
261D4—4882no—
262D4—2442no—
263D4C2×C22⋊D6112yes—
264C2×C4—21no—
265C2×C4—24no—
266C2×C4—612no—
267C2×C4—612no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—4882no—
271C2×C4—4881no—
272C2×C4—2442no—
273C2×C4D4×D6111yescharacteristic
274C2×C4#1175822412yes—
275C2×C4C2×C22⋊D6112yes—
276C2×C4C23×D6111yescharacteristic
277C8—22no—
278C8—1221no—
279C8—1221no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—2441no—
290C22—2441no—
291C22—2441no—
292C22#1451974912yes—
293C22C2×D4×D6111yescharacteristic
294C4—22no—
295C4—1222no—
296C4—1222no—
297C4—2441no—
298C4—2442no—
299C4#1451974912yes—
300C4C22×C22⋊D6111yescharacteristic
301C4C2×#1175822411yescharacteristic
302C2—22no—
303C2—42no—
304C2—82no—
305C2—4881no—
306C2C2×#1451974911yescharacteristic
307C2#1684056611yescharacteristic
308C2#1684057211yescharacteristic
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#3045
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×#14519797C2semidirect
2. #16840329C2semidirect
3. #16840245C2semidirect
4. #16839982C2semidirect
5. #16839975C2semidirect
6. #16839960C2semidirect
7. #16839955C2semidirect
8. #16839790C2semidirect
9. #16839764C2semidirect
10. C2×#14519698C2semidirect
11. C2×AGL(1,ℤ/8)×C61C2semidirect
14. C2×#11758202C22semidirect
15. C2×#11758200C22semidirect
16. C2×#11758201C22semidirect
17. C2×#11758199C22semidirect
24. Q8×Dic61C22semidirect
26. D4×Dic61C22semidirect
31. #14519706C22semidirect
32. #14519706C22semidirect
33. #14519702C22semidirect
34. #14519699C22semidirect
45. #41×C61D4semidirect
155. C2×AGL(1,ℤ/8)D61semidirect
166. C61#3045semidirect
202. #41C22⋊D61semidirect