Finite Group Databasebeta

← #21455085

Subgroups — #21455085

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
2C2×#14519803C211yesmaximal, characteristic, complemented
3C22×#11758199C211yesmaximal, characteristic, complemented
4#16839905C214yesmaximal, complemented
5#16839895C214yesmaximal, complemented
6#16839766C211yesmaximal, characteristic, complemented
7#16839756C211yesmaximal, characteristic, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C61×#535C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226—21no—
13C2×#11758222C2211yescharacteristic
14C2×#11758222C2212yescomplemented
15C22×D244C2211yescharacteristic
16C22×D244C2212yescomplemented
17C2×D4×D61—21no—
18C2×D4×D61—22no—
19#14519803—24no—
20C2×#11758200C2212yescomplemented
21C2×#11758199—24no—
22C2×#11758199C2214yescomplemented
23C2×#11758199C2212yescomplemented
24C2×#11758194C2211yescharacteristic, complemented
25C22×#92418C2211yescharacteristic, complemented
26#14519700C2212yescomplemented
27#14519697C2212yescomplemented
28#14519697C2214yescomplemented
29C22⋊#92418C2214yescomplemented
30C2×#41×C61C2211yescharacteristic
31C22×D4×C61C2211yescharacteristic, complemented
32#127×C61—21no—
33#124×C61—21no—
34#121×C61C2214yescomplemented
35#120×C61—22no—
36#117×C61C2211yescharacteristic, complemented
37C24×C61—21no—
38C23×D61—21no—
39C23×D61—22no—
40#41×C61—22no—
41#41×C61—22no—
42C2×Q8×C61D411yescharacteristic
43C2×D4×C61—24no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—21no—
47C2×D4×C61D412yes—
48C2×D4×C61D411yescharacteristic
49C2×D4×C61C2312yes—
50C22×C4×C61C2312yes—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—22no—
54#11758226—28no—
55D4×D61—216no—
56D4×D61—28no—
57#11758222—22no—
58#11758222—24no—
59#11758222—24no—
60#11758222D414yescomplemented
61C2×D244—21no—
62C2×D244—22no—
63C2×D244—22no—
64C2×D244—24no—
65C2×D244—24no—
66C2×D244D414yescomplemented
67C2×D244C2312yes—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—22no—
71C2×Dic122C2311yescharacteristic
72C4⋊C4×C61C2312yes—
73C22⋊C4×C61—21no—
74C22⋊C4×C61—24no—
75C42×C61—21no—
76#11758200—24no—
77#11758199—28no—
78#11758199—24no—
79#11758194—22no—
80C2×#92418—22no—
81C2×#92418C2312yes—
82C2×#92418C2312yes—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—82no—
86C23×C61C2×D412yes—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89C22×D61—22no—
90C22×D61—28no—
91C22×D61—24no—
92C22×D61—82no—
93C22×D61—84no—
94Q8×C61—22no—
95D4×C61—24no—
96D4×C61—22no—
97D4×C61—22no—
98D4×C61—22no—
99D4×C61—42no—
100D4×C61—84no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2×D412yes—
108C2×C4×C61C2411yescharacteristic
109C22⋊D61—28no—
110C22⋊D61—24no—
111C2×Dic61—21no—
112D244—28no—
113D244—24no—
114D244—21no—
115D244—22no—
116D244C2×D412yes—
117D244C2×D414yes—
118C4×D61—28no—
119C4×D61—24no—
120Dic122—21no—
121Dic122C2×D412yes—
122#92418—22no—
123#92418—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—24no—
127C22×C61—42no—
128C22×C61—44no—
129C22×C61—84no—
130C22×C61#12012yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—24no—
133C2×D61—22no—
134C2×D61—44no—
135C2×D61—42no—
136C2×D61—84no—
137C2×D61—88no—
138C4×C61—22no—
139C4×C61—42no—
140C4×C61#12012yes—
141C4×C61C22×D411yescharacteristic
142C4×C61C22×D411yescharacteristic
143Dic61—22no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61—82no—
148C2×C61C2×#12011yescharacteristic
149C2×C61#57612yes—
150D61—44no—
151D61—42no—
152C2×H(5,𝔽2)—611no—
153C2×AGL(1,ℤ/8)—611no—
154C22×D8—611no—
155#535D6111yescharacteristic, complemented
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—611no—
169C22×D4—612no—
170C22×D4—1222no—
171C22×D4—1221no—
172C22×D4C2×D6111yescharacteristic, complemented
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—614no—
176C2×D8—612no—
177C2×D8—1224no—
178C2×M16—611no—
179C22×C8—611no—
180#127—21no—
181#124—21no—
182#121C2×D6114yescomplemented
183#120—22no—
184#117C2×D6111yescharacteristic, complemented
185#103—612no—
186#102—612no—
187#102—614no—
188C22⋊C8—614no—
189C24—21no—
190C24—1222no—
191C24—1221no—
192#41—22no—
193#41—22no—
194#41—614no—
195#41—1224no—
196#41—1224no—
197#41—1228no—
198#41—1222no—
199C2×Q8—611no—
200C2×Q8C22⋊D6111yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—614no—
206C2×D4—612no—
207C2×D4—611no—
208C2×D4—1224no—
209C2×D4—1224no—
210C2×D4—12216no—
211C2×D4—1228no—
212C2×D4—1222no—
213C2×D4—1221no—
214C2×D4—1222no—
215C2×D4—1222no—
216C2×D4—1221no—
217C2×D4C22⋊D6112yes—
218C2×D4C22⋊D6111yescharacteristic
219C2×D4C22×D6112yes—
220C22×C4—1222no—
221C22×C4—1221no—
222C22×C4C22×D6112yes—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—1228no—
226D8—1224no—
227M16—1222no—
228C2×C8—612no—
229C2×C8—612no—
230C2×C8—1222no—
231C4⋊C4C22×D6112yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—1228no—
239C23—1224no—
240C23—1222no—
241C23—1221no—
242C23—4882no—
243C23—4884no—
244C23C2×C22⋊D6112yes—
245C23C2×C22⋊D6111yescharacteristic
246Q8—22no—
247Q8—612no—
248Q8—1221no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—614no—
256D4—612no—
257D4—1228no—
258D4—1228no—
259D4—1224no—
260D4—1221no—
261D4—1222no—
262D4—1224no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—1228no—
267C2×C4—1221no—
268C2×C4—1224no—
269C2×C4D4×D6112yes—
270C2×C4D4×D6112yes—
271C2×C4C2×C22⋊D6112yes—
272C2×C4C2×C22⋊D6111yescharacteristic
273C2×C4C23×D6111yescharacteristic
274C8—1222no—
275C8—1222no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—1224no—
283C22—1222no—
284C22—4884no—
285C22—4888no—
286C22—2444no—
287C22—2442no—
288C22#1451974512yes—
289C22C22×C22⋊D6111yescharacteristic
290C4—22no—
291C4—42no—
292C4—1222no—
293C4#1451974512yes—
294C4C2×D4×D6111yescharacteristic
295C4C2×D4×D6111yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—2444no—
300C2—2442no—
301C2C2×#1451974511yescharacteristic
302C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#14519803C2semidirect
3. C22×#11758199C2semidirect
4. #16839905C2semidirect
5. #16839895C2semidirect
6. #16839766C2semidirect
7. #16839756C2semidirect
8. #16839729C2semidirect
9. C61×#535C2semidirect
14. C2×#11758222C22semidirect
16. C22×D244C22semidirect
20. C2×#11758200C22semidirect
22. C2×#11758199C22semidirect
23. C2×#11758199C22semidirect
24. C2×#11758194C22semidirect
25. C22×#92418C22semidirect
26. #14519700C22semidirect
27. #14519697C22semidirect
28. #14519697C22semidirect
29. C22⋊#92418C22semidirect
31. C22×D4×C61C22semidirect
34. #121×C61C22semidirect
36. #117×C61C22semidirect
60. #11758222D4semidirect
66. C2×D244D4semidirect
155. #535D61semidirect
161. C61#3008semidirect
172. C22×D4C2×D61semidirect
182. #121C2×D61semidirect
184. #117C2×D61semidirect