Finite Group Databasebeta

← #21455083

Subgroups — #21455083

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×#14519822C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic, complemented
3#16840329C211yesmaximal, characteristic, complemented
4#16839904C214yesmaximal, complemented
5#16839894C214yesmaximal, complemented
6#16839767C211yesmaximal, characteristic, complemented
7#16839759C211yesmaximal, characteristic, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C22×D8×C61C211yesmaximal, characteristic, complemented
10#14519822—24no—
11#14519822—24no—
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C2×#11758224—21no—
15C2×#11758224C2212yescomplemented
16C22×C22⋊D61—22no—
17C2×D4×D61—21no—
18C2×D4×D61C2212yescomplemented
19#14519803—24no—
20C2×#11758200C2212yescomplemented
21C2×#11758199C2212yescomplemented
22C2×#11758194C2211yescharacteristic, complemented
23#14519773—21no—
24#14519764—21no—
25#14519748C2214yescomplemented
26#14519746—22no—
27#14519736C2211yescharacteristic, complemented
28#14519702C2212yescomplemented
29#14519699C2212yescomplemented
30#14519698C2214yescomplemented
31#14519689C2214yescomplemented
32C22×D4×C61C2211yescharacteristic
33C22×D4×C61C2211yescharacteristic, complemented
34C2×D8×C61—24no—
35C2×D8×C61C2214yescomplemented
36C22×C8×C61C2211yescharacteristic, complemented
37C24×C61—21no—
38C24×C61—21no—
39C23×D61—22no—
40C2×D4×C61—21no—
41C2×D4×C61—22no—
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—21no—
45C2×D4×C61D414yescomplemented
46C2×D4×C61C2312yes—
47C2×D4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—216no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61D412yes—
55C22×Dic61—22no—
56#11758224—28no—
57#11758224—24no—
58#11758224—24no—
59D4×D61—28no—
60D4×D61—24no—
61D4×D61—24no—
62#11758222—22no—
63#11758222—22no—
64#11758222—22no—
65#11758222D414yescomplemented
66C2×D244D411yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61C2312yes—
70C2×Dic122D411yescharacteristic
71C2×Dic122C2311yescharacteristic
72D8×C61—28no—
73C2×C8×C61—22no—
74C2×C8×C61C2312yes—
75C22⋊Dic61—21no—
76C22⋊Dic61—24no—
77#11758200—24no—
78#11758199—24no—
79C4⋊Dic61C2312yes—
80C4×Dic61—21no—
81#11758194—22no—
82C2×#92418C2312yes—
83C23×C61—22no—
84C23×C61—24no—
85C23×C61—22no—
86C23×C61—42no—
87C23×C61—82no—
88C23×C61—82no—
89C23×C61C2×D411yescharacteristic
90C22×D61—21no—
91C22×D61—28no—
92C22×D61—84no—
93C22×D61C2×D412yes—
94D4×C61—24no—
95D4×C61—22no—
96D4×C61—22no—
97D4×C61—22no—
98D4×C61—42no—
99D4×C61C2×D414yes—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—28no—
105C22⋊D61—28no—
106C22⋊D61—24no—
107C22⋊D61—24no—
108C22⋊D61—84no—
109C2×Dic61—28no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61C2×D412yes—
113D244—22no—
114D244—21no—
115D244C2×D412yes—
116C4×D61—24no—
117C4×D61—22no—
118C4×D61—22no—
119Dic122—22no—
120Dic122—21no—
121Dic122C2×D412yes—
122C8×C61—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—24no—
126C22×C61—44no—
127C22×C61—42no—
128C22×C61—44no—
129C22×C61—84no—
130C22×C61—84no—
131C22×C61#12012yes—
132C22×C61C22×D411yescharacteristic
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—24no—
136C2×D61—42no—
137C2×D61—88no—
138C4×C61#12012yes—
139C4×C61C22×D411yescharacteristic
140C4×C61C22×D411yescharacteristic
141Dic61—22no—
142Dic61—22no—
143Dic61—42no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—44no—
147C2×C61—82no—
148C2×C61C2×#12011yescharacteristic
149C2×C61#57612yes—
150D61—42no—
151D61—42no—
152C2×H(5,𝔽2)—611no—
153C2×AGL(1,ℤ/8)—611no—
154C22×D8D6111yescharacteristic, complemented
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—611no—
167C2×#41—1221no—
168C22×D4—612no—
169C22×D4—1221no—
170C22×D4—1222no—
171C22×D4C2×D6111yescharacteristic
172C22×D4C2×D6111yescharacteristic, complemented
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—24no—
176C2×D8—612no—
177C2×D8C2×D6114yescomplemented
178C2×M16—611no—
179C22×C8C2×D6111yescharacteristic, complemented
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117—611no—
185#103—612no—
186#102—614no—
187#102—612no—
188C22⋊C8—614no—
189C24—21no—
190C24—21no—
191C24—1222no—
192#41—614no—
193#41—1224no—
194#41—1228no—
195#41—1224no—
196#41—1222no—
197#41—1222no—
198#41—1222no—
199C2×Q8—611no—
200C2×Q8—611no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—612no—
207C2×D4—611no—
208C2×D4—611no—
209C2×D4—1222no—
210C2×D4—1224no—
211C2×D4—1228no—
212C2×D4—1222no—
213C2×D4—12216no—
214C2×D4—1221no—
215C2×D4—1224no—
216C2×D4—1224no—
217C2×D4C22⋊D6114yescomplemented
218C2×D4C22×D6112yes—
219C2×D4C22×D6112yes—
220C22×C4—612no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—28no—
226D8—1224no—
227M16—1222no—
228C2×C8—22no—
229C2×C8—612no—
230C2×C8C22×D6112yes—
231C4⋊C4—612no—
232C22⋊C4—1224no—
233C22⋊C4—1221no—
234C42—1221no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—612no—
242C23—1228no—
243C23—1221no—
244C23—4884no—
245C23D4×D6111yescharacteristic
246Q8—612no—
247Q8—1221no—
248Q8—1222no—
249D4—22no—
250D4—22no—
251D4—22no—
252D4—24no—
253D4—42no—
254D4—612no—
255D4—1228no—
256D4—1228no—
257D4—1224no—
258D4—1224no—
259D4—1221no—
260D4—1222no—
261D4—4884no—
262D4C2×C22⋊D6114yes—
263C2×C4—612no—
264C2×C4—1228no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1224no—
269C2×C4—1222no—
270C2×C4D4×D6112yes—
271C2×C4D4×D6111yescharacteristic
272C2×C4C2×C22⋊D6112yes—
273C2×C4C23×D6111yescharacteristic
274C8—22no—
275C8—1222no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—84no—
283C22—1222no—
284C22—1222no—
285C22—1224no—
286C22—4888no—
287C22—2442no—
288C22#1451974512yes—
289C22C2×D4×D6111yescharacteristic
290C4—1222no—
291C4—1222no—
292C4—2442no—
293C4#1451974512yes—
294C4C2×D4×D6111yescharacteristic
295C4C22×C22⋊D6111yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—2442no—
300C2—2442no—
301C2C2×#1451974511yescharacteristic
302C2#1684056312yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×D8×C61C2
socleC22×C61C22×D4
hypercenterC22×D8D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14519822C2semidirect
2. C2×#14519803C2semidirect
3. #16840329C2semidirect
4. #16839904C2semidirect
5. #16839894C2semidirect
6. #16839767C2semidirect
7. #16839759C2semidirect
8. #16839728C2semidirect
9. C22×D8×C61C2semidirect
15. C2×#11758224C22semidirect
18. C2×D4×D61C22semidirect
20. C2×#11758200C22semidirect
21. C2×#11758199C22semidirect
22. C2×#11758194C22semidirect
25. #14519748C22semidirect
27. #14519736C22semidirect
28. #14519702C22semidirect
29. #14519699C22semidirect
30. #14519698C22semidirect
31. #14519689C22semidirect
33. C22×D4×C61C22semidirect
35. C2×D8×C61C22semidirect
36. C22×C8×C61C22semidirect
45. C2×D4×C61D4semidirect
65. #11758222D4semidirect
154. C22×D8D61semidirect
161. C61#3008semidirect
172. C22×D4C2×D61semidirect
177. C2×D8C2×D61semidirect
179. C22×C8C2×D61semidirect
217. C2×D4C22⋊D61semidirect