Finite Group Databasebeta

← #21456296

Subgroups — #21456296

Order 7808.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519807C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic, complemented
3C22×#11758190C211yesmaximal, characteristic, complemented
4#16840333C211yesmaximal, characteristic, complemented
5#16840326C211yesmaximal, characteristic, complemented
6#16840155C212yesmaximal, complemented
7#16840150C212yesmaximal, complemented
8#16840143C212yesmaximal, complemented
9#16840133C212yesmaximal, complemented
10#16839717C211yesmaximal, characteristic, complemented
11C2×#135×C61C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14#14519807—24no—
15#14519802—24no—
16C2×#11758202C2212yescomplemented
17C2×#11758190—24no—
18C2×#11758190C2212yes—
19C2×#11758190C2212yes—
20C2×#11758200C2212yescomplemented
21C2×#11758201C2212yes—
22C2×#11758199C2212yes—
23C2×#11758194C2211yescharacteristic
24#14519775C2212yescomplemented
25#14519773C2212yes—
26#14519766C2212yes—
27#14519764C2212yescomplemented
28#14519758—22no—
29#14519756—22no—
30#14519751—22no—
31#14519745—22no—
32#14519736C2211yescharacteristic
33#14519687C2212yescomplemented
34C8×Dic61C2212yescomplemented
35C2×#41×C61C2211yescharacteristic
36C2×#41×C61C2211yescharacteristic
37#135×C61—24no—
38C2×Q16×C61C2211yescharacteristic, complemented
39C2×SD16×C61C2211yescharacteristic, complemented
40C2×SD16×C61C2211yescharacteristic, complemented
41C2×D8×C61C2211yescharacteristic, complemented
42C22×C8×C61C2211yescharacteristic
43C23×D61—21no—
44#41×C61—22no—
45#41×C61—22no—
46#41×C61—22no—
47#41×C61—22no—
48C2×Q8×C61C2311yescharacteristic
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61—21no—
52C2×D4×C61C2311yescharacteristic
53C2×D4×C61C2311yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C2311yescharacteristic
57C2×C22⋊D61—24no—
58C22×Dic61—21no—
59C2×D244—22no—
60C2×D244—22no—
61C2×D244—21no—
62C2×D244C2312yes—
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—21no—
66C2×Dic122C2312yes—
67Q16×C61—22no—
68SD16×C61—22no—
69SD16×C61—22no—
70D8×C61—22no—
71C2×C8×C61D414yescomplemented
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C22⋊Dic61—24no—
75C22⋊Dic61D412yes—
76#11758202—24no—
77#11758201—24no—
78#11758200—24no—
79#11758199—24no—
80#11758198—24no—
81C4⋊Dic61D412yes—
82#11758196—24no—
83C4×Dic61C2312yes—
84#11758194D414yescomplemented
85C2×#92418C2312yes—
86#11758190—24no—
87#11758190—24no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61C2×D411yescharacteristic
91C22×D61—22no—
92C22×D61—42no—
93C22×D61—82no—
94Q8×C61—21no—
95Q8×C61—21no—
96Q8×C61—21no—
97Q8×C61—21no—
98D4×C61—21no—
99D4×C61—21no—
100D4×C61—21no—
101D4×C61—21no—
102D4×C61—42no—
103D4×C61—42no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D412yes—
110C2×C4×C61C2×D412yes—
111C2×C4×C61C2411yescharacteristic
112C22⋊D61—84no—
113C2×Dic61—22no—
114C2×Dic61—42no—
115C2×Dic61C2×D414yes—
116D244—22no—
117D244—22no—
118D244—42no—
119Dic122—22no—
120Dic122—22no—
121Dic122—42no—
122C8×C61C2×D412yes—
123C8×C61C2×D412yes—
124#92418C2×D414yes—
125C22×C61—22no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61#12712yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—42no—
133C2×D61—44no—
134C2×D61—84no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61#12712yes—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—24no—
141Dic61—42no—
142#3154—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61—81no—
146C2×C61C2×#12711yescharacteristic
147C2×C61#57712yes—
148D61—82no—
149C2×#137—611no—
150C2×AGL(1,ℤ/8)—611no—
151C2×#135D6111yescharacteristic, complemented
152C22×SD16—611no—
153#536—611no—
154#535—611no—
155#497—612no—
156#496—612no—
157#495—612no—
158#492—612no—
159#405—611no—
160C61#315411yescharacteristic, complemented, Sylow
161C2×#41C2×D6111yescharacteristic
162C2×#41C2×D6111yescharacteristic
163C22×Q8—611no—
164C22×D4—611no—
165#137—1224no—
166AGL(1,ℤ/8)—1224no—
167#135—24no—
168C2×Q16—612no—
169C2×Q16C2×D6111yescharacteristic, complemented
170C2×SD16—612no—
171C2×SD16—612no—
172C2×SD16—612no—
173C2×SD16—612no—
174C2×SD16—1224no—
175C2×SD16C2×D6111yescharacteristic, complemented
176C2×SD16C2×D6111yescharacteristic, complemented
177C2×D8—612no—
178C2×D8C2×D6111yescharacteristic, complemented
179C2×M16—611no—
180C22×C8C2×D6111yescharacteristic
181C4⋊Q8—612no—
182#127—612no—
183#124—612no—
184#124—612no—
185#123—1222no—
186C22⋊Q8—1222no—
187#121—1222no—
188#120—1222no—
189#117—611no—
190#97—612no—
191C4×C8—612no—
192C24—1221no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—612no—
198C2×Q8—1221no—
199C2×Q8—1222no—
200C2×Q8—1222no—
201C2×Q8C22×D6111yescharacteristic
202C2×Q8C22×D6111yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—612no—
206C2×D4—1224no—
207C2×D4—1222no—
208C2×D4—1221no—
209C2×D4—1222no—
210C2×D4C22×D6111yescharacteristic
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—1221no—
215C22×C4C22×D6111yescharacteristic
216Q16—22no—
217Q16—1224no—
218SD16—22no—
219SD16—22no—
220SD16—1224no—
221SD16—1224no—
222SD16—1224no—
223SD16—1224no—
224D8—22no—
225D8—1224no—
226M16—614no—
227C2×C8—612no—
228C2×C8C22⋊D6114yescomplemented
229C2×C8C22×D6111yescharacteristic
230C2×C8C22×D6111yescharacteristic
231C4⋊C4—612no—
232C4⋊C4—1224no—
233C22⋊C4—612no—
234C22⋊C4—1224no—
235C22⋊C4—1224no—
236C42—612no—
237C23—21no—
238C23—21no—
239C23—1222no—
240C23—4882no—
241C23—2442no—
242C23D4×D6111yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—1222no—
248Q8—1222no—
249Q8—2442no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—1222no—
257D4—1222no—
258D4—4884no—
259D4—2442no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—614no—
265C2×C4—1222no—
266C2×C4—2442no—
267C2×C4D4×D6112yes—
268C2×C4D4×D6111yescharacteristic
269C2×C4C2×C22⋊D6112yes—
270C2×C4C23×D6111yescharacteristic
271C8—614no—
272C8C2×C22⋊D6112yes—
273C8C2×C22⋊D6112yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—4884no—
280C22—2442no—
281C22—2444no—
282C22#1451977312yes—
283C22C2×D4×D6111yescharacteristic
284C4—41no—
285C4—41no—
286C4—1224no—
287C4—2442no—
288C4#1451977312yes—
289C4C2×D4×D6111yescharacteristic
290C4C22×C22⋊D6111yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—4882no—
295C2C2×#1451977311yescharacteristic
296C2#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×#14519802C2semidirect
3. C22×#11758190C2semidirect
4. #16840333C2semidirect
5. #16840326C2semidirect
6. #16840155C2semidirect
7. #16840150C2semidirect
8. #16840143C2semidirect
9. #16840133C2semidirect
10. #16839717C2semidirect
11. C2×#135×C61C2semidirect
16. C2×#11758202C22semidirect
20. C2×#11758200C22semidirect
24. #14519775C22semidirect
27. #14519764C22semidirect
33. #14519687C22semidirect
34. C8×Dic61C22semidirect
38. C2×Q16×C61C22semidirect
39. C2×SD16×C61C22semidirect
40. C2×SD16×C61C22semidirect
41. C2×D8×C61C22semidirect
71. C2×C8×C61D4semidirect
84. #11758194D4semidirect
151. C2×#135D61semidirect
160. C61#3154semidirect
169. C2×Q16C2×D61semidirect
175. C2×SD16C2×D61semidirect
176. C2×SD16C2×D61semidirect
178. C2×D8C2×D61semidirect
228. C2×C8C22⋊D61semidirect