Finite Group Databasebeta

← #21455086

Subgroups — #21455086

Order 7808.

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

normal subgroups only

This group has 784 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×#14519823C211yesmaximal, characteristic, complemented
2C22×#11758199C211yesmaximal, characteristic, complemented
3#16840329C211yesmaximal, characteristic, complemented
4#16839906C214yesmaximal, complemented
5#16839894C214yesmaximal, complemented
6#16839768C211yesmaximal, characteristic, complemented
7#16839758C211yesmaximal, characteristic, complemented
8#16839730C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226C2212yescomplemented
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C22×D244—21no—
16C22×D244C2211yescharacteristic
17C2×D4×D61—22no—
18C2×D4×D61C2212yescomplemented
19C2×#11758199—24no—
20C2×#11758199C2214yescomplemented
21C22×#92418C2211yescharacteristic, complemented
22#14519773—21no—
23#14519764—21no—
24#14519748C2214yescomplemented
25#14519746—22no—
26#14519736C2211yescharacteristic, complemented
27#14519701C2212yescomplemented
28#14519699C2214yescomplemented
29#14519698C2212yescomplemented
30#14519689C2214yescomplemented
31C2×#41×C61C2211yescharacteristic
32C22×D4×C61C2211yescharacteristic, complemented
33AGL(1,ℤ/8)×C61—24no—
34C2×SD16×C61C2212yescomplemented
35C2×D8×C61C2212yescomplemented
36C2×M16×C61C2211yescharacteristic, complemented
37C24×C61—21no—
38C23×D61—21no—
39C23×D61—22no—
40#41×C61—22no—
41#41×C61D414yescomplemented
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—21no—
47C2×D4×C61C2312yes—
48C2×D4×C61C2311yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—24no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61D412yes—
54#11758226—24no—
55#11758226—24no—
56D4×D61—216no—
57D4×D61—24no—
58D4×D61—24no—
59#11758222—28no—
60#11758222—22no—
61#11758222—22no—
62C2×D244—28no—
63C2×D244—22no—
64C2×D244—21no—
65C2×D244—22no—
66C2×D244D411yescharacteristic
67C2×D244D414yescomplemented
68C2×D244C2312yes—
69C2×C4×D61—22no—
70C2×C4×D61C2312yes—
71C2×Dic122D411yescharacteristic
72SD16×C61—24no—
73D8×C61—24no—
74M16×C61—22no—
75C2×C8×C61C2312yes—
76C22⋊Dic61—21no—
77C22⋊Dic61—24no—
78#11758199—28no—
79C4⋊Dic61C2312yes—
80C4×Dic61—21no—
81C2×#92418—22no—
82C2×#92418C2312yes—
83C23×C61—21no—
84C23×C61—22no—
85C23×C61—42no—
86C23×C61—82no—
87C23×C61C2×D411yescharacteristic
88C22×D61—22no—
89C22×D61—28no—
90C22×D61—24no—
91C22×D61—84no—
92C22×D61—82no—
93C22×D61C2×D412yes—
94Q8×C61—21no—
95Q8×C61C2×D412yes—
96D4×C61—24no—
97D4×C61—21no—
98D4×C61—22no—
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×C61C2×D412yes—
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—28no—
109C22⋊D61—24no—
110C22⋊D61—84no—
111C2×Dic61—22no—
112C2×Dic61C2×D412yes—
113D244—28no—
114D244—22no—
115D244—24no—
116D244—22no—
117D244C2×D414yes—
118C4×D61—28no—
119C4×D61—22no—
120C4×D61—22no—
121Dic122—22no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—44no—
129C22×C61—84no—
130C22×C61#12012yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—22no—
133C2×D61—24no—
134C2×D61—24no—
135C2×D61—44no—
136C2×D61—84no—
137C2×D61—88no—
138C4×C61—22no—
139C4×C61#12012yes—
140C4×C61C22×D411yescharacteristic
141C4×C61C22×D411yescharacteristic
142Dic61—22no—
143Dic61—42no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61—82no—
148C2×C61C2×#12011yescharacteristic
149C2×C61#57612yes—
150D61—42no—
151D61—44no—
152C2×H(5,𝔽2)—611no—
153C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
154C22×D8—611no—
155#535—611no—
156#449—614no—
157#447—614no—
158#418—611no—
159#416—611no—
160#408—611no—
161C61#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1224no—
163H(5,𝔽2)—1224no—
164C2×#41—611no—
165C2×#41—612no—
166C2×#41—1221no—
167C2×#41C2×D6111yescharacteristic
168C22×D4—612no—
169C22×D4—611no—
170C22×D4—1221no—
171C22×D4—1222no—
172C22×D4C2×D6111yescharacteristic, complemented
173AGL(1,ℤ/8)—24no—
174C2×SD16C2×D6112yescomplemented
175C2×D8—614no—
176C2×D8—1224no—
177C2×D8C2×D6112yescomplemented
178C2×M16C2×D6111yescharacteristic, complemented
179C22×C8—611no—
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117—611no—
185#103—612no—
186#102—612no—
187#102—614no—
188C22⋊C8—614no—
189C24—21no—
190C24—1222no—
191C24—1221no—
192#41—22no—
193#41—1228no—
194#41—1224no—
195#41—1224no—
196#41—1222no—
197#41—1222no—
198#41C22⋊D6114yescomplemented
199C2×Q8—611no—
200C2×Q8C22×D6111yescharacteristic
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—612no—
206C2×D4—614no—
207C2×D4—611no—
208C2×D4—612no—
209C2×D4—1222no—
210C2×D4—1228no—
211C2×D4—1222no—
212C2×D4—1224no—
213C2×D4—12216no—
214C2×D4—1224no—
215C2×D4—1224no—
216C2×D4—1221no—
217C2×D4—1222no—
218C2×D4C22×D6112yes—
219C2×D4C22×D6111yescharacteristic
220C22×C4—21no—
221C22×C4—612no—
222C22×C4—1222no—
223C22×C4C22×D6111yescharacteristic
224SD16—24no—
225D8—24no—
226D8—1228no—
227M16—22no—
228C2×C8—612no—
229C2×C8—1222no—
230C2×C8C22×D6112yes—
231C4⋊C4—612no—
232C22⋊C4—1224no—
233C22⋊C4—1221no—
234C42—1221no—
235C23—21no—
236C23—22no—
237C23—42no—
238C23—82no—
239C23—612no—
240C23—1228no—
241C23—1224no—
242C23—1222no—
243C23—4882no—
244C23—4884no—
245C23D4×D6111yescharacteristic
246Q8—21no—
247Q8—1222no—
248Q8C2×C22⋊D6112yes—
249D4—24no—
250D4—21no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—614no—
255D4—1228no—
256D4—1228no—
257D4—1224no—
258D4—1222no—
259D4—1224no—
260D4—1222no—
261D4—4884no—
262D4C2×C22⋊D6112yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—612no—
266C2×C4—1228no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4D4×D6112yes—
271C2×C4D4×D6111yescharacteristic
272C2×C4C2×C22⋊D6112yes—
273C2×C4C23×D6111yescharacteristic
274C8—22no—
275C8—1222no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—1224no—
283C22—1222no—
284C22—1224no—
285C22—4884no—
286C22—4888no—
287C22—2444no—
288C22#1451974512yes—
289C22C2×D4×D6111yescharacteristic
290C4—22no—
291C4—1222no—
292C4—2442no—
293C4#1451974512yes—
294C4C2×D4×D6111yescharacteristic
295C4C22×C22⋊D6111yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—2442no—
300C2—2444no—
301C2C2×#1451974511yescharacteristic
302C2#1684056612yes—
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#3008
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×#14519823C2semidirect
2. C22×#11758199C2semidirect
3. #16840329C2semidirect
4. #16839906C2semidirect
5. #16839894C2semidirect
6. #16839768C2semidirect
7. #16839758C2semidirect
8. #16839730C2semidirect
9. C2×AGL(1,ℤ/8)×C61C2semidirect
12. C2×#11758226C22semidirect
18. C2×D4×D61C22semidirect
20. C2×#11758199C22semidirect
21. C22×#92418C22semidirect
24. #14519748C22semidirect
26. #14519736C22semidirect
27. #14519701C22semidirect
28. #14519699C22semidirect
29. #14519698C22semidirect
30. #14519689C22semidirect
32. C22×D4×C61C22semidirect
34. C2×SD16×C61C22semidirect
35. C2×D8×C61C22semidirect
36. C2×M16×C61C22semidirect
41. #41×C61D4semidirect
67. C2×D244D4semidirect
153. C2×AGL(1,ℤ/8)D61semidirect
161. C61#3008semidirect
172. C22×D4C2×D61semidirect
174. C2×SD16C2×D61semidirect
177. C2×D8C2×D61semidirect
178. C2×M16C2×D61semidirect
198. #41C22⋊D61semidirect