Finite Group Databasebeta

← #21456291

Subgroups — #21456291

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×#14519803C211yesmaximal, characteristic, complemented
3C2×#14519797C211yesmaximal, characteristic, complemented
4C22×#11758200C211yesmaximal, characteristic, complemented
5#16840338C211yesmaximal, characteristic, complemented
6#16840157C212yesmaximal, complemented
7#16840149C212yesmaximal, complemented
8#16840144C212yesmaximal, complemented
9#16840134C212yesmaximal, complemented
10#16839718C211yesmaximal, characteristic, complemented
11C61×#535C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14#14519807—24no—
15#14519803—24no—
16#14519797—24no—
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758202C2212yescomplemented
19C2×#11758200—24no—
20C2×#11758200C2212yes—
21C2×#11758200C2212yes—
22C2×#11758200C2212yes—
23C2×#11758200C2211yescharacteristic, complemented
24C2×#11758200C2212yescomplemented
25C2×#11758201C2211yescharacteristic, complemented
26C2×#11758199C2212yes—
27C2×#11758199C2211yescharacteristic, complemented
28C2×#11758194C2211yescharacteristic
29C22×#92418C2211yescharacteristic
30#14519777C2212yescomplemented
31#14519765C2212yescomplemented
32#14519761—22no—
33#14519757—22no—
34#14519688C2212yescomplemented
35C4×#92418C2212yescomplemented
36C2×#41×C61C2211yescharacteristic
37C22×D4×C61C2211yescharacteristic
38#127×C61C2212yes—
39#124×C61C2212yes—
40#121×C61—22no—
41#120×C61—22no—
42#117×C61C2211yescharacteristic
43C24×C61—21no—
44#41×C61—22no—
45#41×C61—22no—
46C2×Q8×C61C2311yescharacteristic
47C2×D4×C61—21no—
48C2×D4×C61—22no—
49C2×D4×C61—22no—
50C2×D4×C61—21no—
51C2×D4×C61—24no—
52C2×D4×C61C2312yes—
53C2×D4×C61C2311yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61C2311yescharacteristic
56C2×C22⋊D61—21no—
57C22×Dic61—21no—
58#11758222—22no—
59#11758222—22no—
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—21no—
65C2×Dic122C2312yes—
66C2×Dic122C2311yescharacteristic
67C4⋊C4×C61D412yes—
68C22⋊C4×C61—24no—
69C22⋊C4×C61D412yes—
70C42×C61C2312yes—
71#11758202—22no—
72#11758202—24no—
73#11758201—22no—
74#11758200—24no—
75#11758200—24no—
76#11758200—24no—
77#11758200—22no—
78#11758200—24no—
79#11758199—24no—
80#11758199—22no—
81#11758198—24no—
82C4⋊Dic61—24no—
83#11758194D414yescomplemented
84C2×#92418D414yescomplemented
85C2×#92418C2311yescharacteristic
86C2×#92418C2312yes—
87C2×#92418C2311yescharacteristic
88C23×C61—22no—
89C23×C61—21no—
90C23×C61—42no—
91C23×C61—82no—
92C23×C61C2×D411yescharacteristic
93C22×D61—21no—
94Q8×C61—21no—
95Q8×C61—21no—
96D4×C61—22no—
97D4×C61—21no—
98D4×C61—22no—
99D4×C61—21no—
100D4×C61—42no—
101D4×C61—42no—
102D4×C61—84no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61C2×D414yes—
106C2×C4×C61C2×D411yescharacteristic
107C2×C4×C61C2×D412yes—
108C2×C4×C61C2×D412yes—
109C2×C4×C61C2411yescharacteristic
110C22⋊D61—42no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—42no—
114D244—21no—
115D244—21no—
116C4×D61—42no—
117Dic122—22no—
118Dic122—21no—
119Dic122—22no—
120Dic122—21no—
121Dic122—42no—
122#92418C2×D412yes—
123#92418C2×D412yes—
124#92418C2×D414yes—
125C22×C61—22no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—44no—
130C22×C61—84no—
131C22×C61#12712yes—
132C22×C61C22×D411yescharacteristic
133C2×D61—41no—
134C2×D61—42no—
135C4×C61—24no—
136C4×C61—41no—
137C4×C61#12712yes—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—42no—
141Dic61—41no—
142#3154—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61—82no—
146C2×C61C2×#12711yescharacteristic
147C2×C61#57712yes—
148D61—81no—
149C2×#137—611no—
150C2×AGL(1,ℤ/8)—611no—
151C2×#135—611no—
152C22×SD16—611no—
153#536—611no—
154#535D6111yescharacteristic, complemented
155#497—612no—
156#496—612no—
157#495—612no—
158#492—612no—
159#405—611no—
160C61#315411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8—611no—
164C22×D4C2×D6111yescharacteristic
165#137—1224no—
166AGL(1,ℤ/8)—1224no—
167#135—1224no—
168C2×Q16—611no—
169C2×Q16—612no—
170C2×SD16—611no—
171C2×SD16—612no—
172C2×SD16—612no—
173C2×SD16—611no—
174C2×SD16—612no—
175C2×SD16—612no—
176C2×SD16—1224no—
177C2×D8—611no—
178C2×D8—612no—
179C2×M16—611no—
180C22×C8—611no—
181C4⋊Q8—612no—
182#127C2×D6112yes—
183#124—612no—
184#124C2×D6112yes—
185#123—1222no—
186C22⋊Q8—1222no—
187#121—22no—
188#120—22no—
189#117C2×D6111yescharacteristic
190#97—612no—
191C4×C8—612no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—1222no—
196#41—1222no—
197C2×Q8—612no—
198C2×Q8—611no—
199C2×Q8—1221no—
200C2×Q8—1222no—
201C2×Q8—1222no—
202C2×Q8C22×D6111yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—611no—
209C2×D4—1221no—
210C2×D4C22×D6112yes—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4C22×D6111yescharacteristic
216Q16—1222no—
217Q16—1224no—
218SD16—1224no—
219SD16—1224no—
220SD16—1222no—
221SD16—1224no—
222SD16—1224no—
223SD16—1222no—
224D8—1222no—
225D8—1224no—
226M16—614no—
227C2×C8—614no—
228C2×C8—611no—
229C2×C8—612no—
230C2×C8—611no—
231C4⋊C4—1224no—
232C4⋊C4C22⋊D6112yes—
233C22⋊C4—24no—
234C22⋊C4—1224no—
235C22⋊C4C22⋊D6112yes—
236C42C22×D6112yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—1221no—
242C23C2×C22⋊D6111yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—1222no—
246Q8—1221no—
247Q8—1222no—
248Q8—1221no—
249Q8—2442no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—1221no—
258D4—1221no—
259D4—2442no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4D4×D6112yes—
267C2×C4D4×D6112yes—
268C2×C4C2×C22⋊D6114yes—
269C2×C4C2×C22⋊D6111yescharacteristic
270C2×C4C23×D6111yescharacteristic
271C8—612no—
272C8—612no—
273C8—614no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—2441no—
281C22—2442no—
282C22#1451977312yes—
283C22C22×C22⋊D6111yescharacteristic
284C4—24no—
285C4—41no—
286C4—2441no—
287C4—2442no—
288C4#1451977312yes—
289C4C2×D4×D6111yescharacteristic
290C4C2×D4×D6111yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—4881no—
295C2C2×#1451977311yescharacteristic
296C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×#14519803C2semidirect
3. C2×#14519797C2semidirect
4. C22×#11758200C2semidirect
5. #16840338C2semidirect
6. #16840157C2semidirect
7. #16840149C2semidirect
8. #16840144C2semidirect
9. #16840134C2semidirect
10. #16839718C2semidirect
11. C61×#535C2semidirect
17. C2×#11758202C22semidirect
18. C2×#11758202C22semidirect
23. C2×#11758200C22semidirect
24. C2×#11758200C22semidirect
25. C2×#11758201C22semidirect
27. C2×#11758199C22semidirect
30. #14519777C22semidirect
31. #14519765C22semidirect
34. #14519688C22semidirect
35. C4×#92418C22semidirect
83. #11758194D4semidirect
84. C2×#92418D4semidirect
154. #535D61semidirect
160. C61#3154semidirect