Finite Group Databasebeta

← #21456267

Subgroups — #21456267

Order 7808.

656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic, complemented
3C2×#14519802C211yesmaximal, characteristic, complemented
4#16840308C211yesmaximal, characteristic, complemented
5C2×#14519773C211yesmaximal, characteristic, complemented
6#16840150C212yesmaximal, complemented
7#16840148C212yesmaximal, complemented
8#16840137C212yesmaximal, complemented
9#16840133C212yesmaximal, complemented
10M16×Dic61C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C22⋊D61—22no—
15#14519805—24no—
16#14519803—24no—
17#14519802—24no—
18C2×#11758190C2212yescomplemented
19C2×#11758200C2212yescomplemented
20C2×#11758201C2212yescomplemented
21C2×D488C2212yescomplemented
22C2×#11758199C2212yescomplemented
23C2×#11758199C2212yescomplemented
24C2×#11758194C2211yescharacteristic
25#14519775C2211yescharacteristic, complemented
26#14519773—22no—
27#14519773C2212yes—
28#14519773C2212yes—
29#14519773C2211yescharacteristic, complemented
30#14519766C2211yescharacteristic, complemented
31#14519764C2211yescharacteristic, complemented
32#14519749—22no—
33C4×C22⋊D61—22no—
34C2×C4×Dic61C2211yescharacteristic
35#14519687C2212yescomplemented
36C8×Dic61C2212yescomplemented
37C2×#41×C61C2211yescharacteristic
38C22×D4×C61C2211yescharacteristic
39AGL(1,ℤ/8)×C61—24no—
40C2×SD16×C61C2212yescomplemented
41C2×D8×C61C2212yescomplemented
42C2×M16×C61C2211yescharacteristic
43C24×C61—21no—
44C23×D61—21no—
45#41×C61—22no—
46#41×C61—22no—
47C2×Q8×C61C2311yescharacteristic
48C2×D4×C61—21no—
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C2×D4×C61—21no—
52C2×D4×C61C2311yescharacteristic
53C2×D4×C61C2312yes—
54C22×C4×C61—21no—
55C22×C4×C61C2311yescharacteristic
56C2×C22⋊D61—21no—
57C2×C22⋊D61—24no—
58C2×C22⋊D61—24no—
59C2×C22⋊D61—22no—
60C2×C22⋊D61—48no—
61C22×Dic61D412yes—
62#11758222—22no—
63#11758222—22no—
64C2×D244—22no—
65C2×D244—22no—
66C2×D244—21no—
67C2×D244C2312yes—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×Dic122C2311yescharacteristic
71SD16×C61—24no—
72D8×C61—24no—
73M16×C61D414yescomplemented
74C2×C8×C61C2312yes—
75C22⋊Dic61—22no—
76#11758201—24no—
77#11758200—24no—
78#11758199—24no—
79#11758199—24no—
80#11758198—22no—
81#11758196—22no—
82C4×Dic61D412yes—
83C4×Dic61C2311yescharacteristic
84C4×Dic61C2311yescharacteristic
85#11758194D414yescomplemented
86C2×#92418C2312yes—
87D488—24no—
88#11758190—24no—
89C23×C61—21no—
90C23×C61—22no—
91C23×C61—44no—
92C23×C61—42no—
93C23×C61C2×D411yescharacteristic
94C22×D61—21no—
95C22×D61—22no—
96C22×D61—44no—
97C22×D61—42no—
98Q8×C61—21no—
99Q8×C61—21no—
100D4×C61—21no—
101D4×C61—22no—
102D4×C61—21no—
103D4×C61—22no—
104D4×C61—42no—
105D4×C61—42no—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D412yes—
110C2×C4×C61C2×D412yes—
111C2×C4×C61C2411yescharacteristic
112C22⋊D61—48no—
113C22⋊D61—42no—
114C22⋊D61—44no—
115C22⋊D61—48no—
116C2×Dic61—24no—
117C2×Dic61—21no—
118C2×Dic61C2×D412yes—
119C2×Dic61C2×D412yes—
120D244—22no—
121D244—21no—
122D244—21no—
123D244—22no—
124D244—42no—
125C4×D61—42no—
126Dic122—21no—
127Dic122—21no—
128C8×C61C2×D414yescomplemented
129#92418C2×D414yescomplemented
130C22×C61—22no—
131C22×C61—41no—
132C22×C61—42no—
133C22×C61—44no—
134C22×C61—42no—
135C22×C61—84no—
136C22×C61#12712yes—
137C22×C61C22×D411yescharacteristic
138C2×D61—41no—
139C2×D61—42no—
140C2×D61—44no—
141C2×D61—42no—
142C2×D61—84no—
143C4×C61—41no—
144C4×C61#12712yes—
145C4×C61C22×D411yescharacteristic
146C4×C61C22×D411yescharacteristic
147Dic61—22no—
148Dic61—41no—
149Dic61AGL(1,ℤ/8)14yescomplemented
150#3151—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—81no—
153C2×C61—82no—
154C2×C61C2×#12711yescharacteristic
155C2×C61C2×AGL(1,ℤ/8)12yes—
156D61—81no—
157D61—82no—
158C2×AGL(1,ℤ/8)—611no—
159C2×AGL(1,ℤ/8)—611no—
160C2×AGL(1,ℤ/8)—611no—
161C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
162#532—611no—
163C2×#127—611no—
164#496—612no—
165#496—612no—
166#493—612no—
167#492—612no—
168C4×M16—611no—
169C61#315111yescharacteristic, complemented, Sylow
170C2×#41—611no—
171C2×#41C2×D6111yescharacteristic
172C22×D4—611no—
173C22×D4—1222no—
174C22×D4C2×D6111yescharacteristic
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—1224no—
177AGL(1,ℤ/8)—1224no—
178AGL(1,ℤ/8)—1224no—
179C2×SD16—612no—
180C2×SD16—612no—
181C2×SD16—612no—
182C2×SD16C2×D6112yescomplemented
183C2×D8—612no—
184C2×D8—612no—
185C2×D8—612no—
186C2×D8C2×D6112yescomplemented
187C2×M16—611no—
188C2×M16C2×D6111yescharacteristic
189C4⋊Q8—611no—
190#127—612no—
191#127—612no—
192#127—611no—
193#127—1222no—
194#124—611no—
195#124—611no—
196#121—1222no—
197C4×D4—1222no—
198C2×C42—611no—
199#97—612no—
200C4×C8—612no—
201C24—21no—
202C24—1221no—
203#41—22no—
204#41—22no—
205#41—1222no—
206#41—1222no—
207C2×Q8—611no—
208C2×Q8C22×D6111yescharacteristic
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—611no—
214C2×D4—612no—
215C2×D4—1222no—
216C2×D4—1224no—
217C2×D4—1224no—
218C2×D4—1221no—
219C2×D4—1222no—
220C2×D4—1221no—
221C2×D4—1222no—
222C2×D4—2448no—
223C2×D4C22×D6111yescharacteristic
224C2×D4C22×D6112yes—
225C22×C4—21no—
226C22×C4—612no—
227C22×C4—1221no—
228C22×C4C22×D6111yescharacteristic
229SD16—24no—
230SD16—1224no—
231SD16—1224no—
232SD16—1224no—
233D8—24no—
234D8—1224no—
235D8—1224no—
236D8—1224no—
237M16—614no—
238M16C22⋊D6114yescomplemented
239C2×C8—612no—
240C2×C8C22×D6112yes—
241C4⋊C4—1222no—
242C22⋊C4—1222no—
243C22⋊C4—1222no—
244C42—612no—
245C42—611no—
246C42—611no—
247C23—21no—
248C23—22no—
249C23—44no—
250C23—42no—
251C23—1221no—
252C23—1222no—
253C23—2444no—
254C23—2442no—
255C23D4×D6111yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—1221no—
259Q8—1221no—
260D4—21no—
261D4—22no—
262D4—21no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—1221no—
267D4—1222no—
268D4—1221no—
269D4—1222no—
270D4—2444no—
271D4—2448no—
272D4—2448no—
273D4—2442no—
274D4—2442no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—1224no—
280C2×C4—1221no—
281C2×C4—2442no—
282C2×C4D4×D6112yes—
283C2×C4D4×D6111yescharacteristic
284C2×C4C2×C22⋊D6112yes—
285C2×C4C23×D6111yescharacteristic
286C8—614no—
287C8C2×C22⋊D6114yescomplemented
288C22—22no—
289C22—44no—
290C22—42no—
291C22—41no—
292C22—42no—
293C22—84no—
294C22—4884no—
295C22—2444no—
296C22—2442no—
297C22—2441no—
298C22—2442no—
299C22#1451977312yes—
300C22C2×D4×D6111yescharacteristic
301C4—41no—
302C4—614no—
303C4—1222no—
304C4—2441no—
305C4#1451977312yes—
306C4C2×D4×D6111yescharacteristic
307C4C22×C22⋊D6111yescharacteristic
308C2—22no—
309C2—82no—
310C2—81no—
311C2—4882no—
312C2—4881no—
313C2C2×#1451977311yescharacteristic
314C2AGL(1,ℤ/8)×D6112yes—
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#3151
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×#14519805C2semidirect
2. C2×#14519803C2semidirect
3. C2×#14519802C2semidirect
4. #16840308C2semidirect
5. C2×#14519773C2semidirect
6. #16840150C2semidirect
7. #16840148C2semidirect
8. #16840137C2semidirect
9. #16840133C2semidirect
10. M16×Dic61C2semidirect
11. C2×AGL(1,ℤ/8)×C61C2semidirect
18. C2×#11758190C22semidirect
19. C2×#11758200C22semidirect
20. C2×#11758201C22semidirect
21. C2×D488C22semidirect
22. C2×#11758199C22semidirect
23. C2×#11758199C22semidirect
25. #14519775C22semidirect
29. #14519773C22semidirect
30. #14519766C22semidirect
31. #14519764C22semidirect
35. #14519687C22semidirect
36. C8×Dic61C22semidirect
40. C2×SD16×C61C22semidirect
41. C2×D8×C61C22semidirect
73. M16×C61D4semidirect
85. #11758194D4semidirect
128. C8×C61C2×D4semidirect
129. #92418C2×D4semidirect
149. Dic61AGL(1,ℤ/8)semidirect
161. C2×AGL(1,ℤ/8)D61semidirect
169. C61#3151semidirect
182. C2×SD16C2×D61semidirect
186. C2×D8C2×D61semidirect
238. M16C22⋊D61semidirect
287. C8C2×C22⋊D61semidirect