Finite Group Databasebeta

← #21455501

Subgroups — #21455501

Order 7808.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519802C211yesmaximal, characteristic, complemented
2C2×#14519784C211yesmaximal, characteristic, complemented
3#16840326C211yesmaximal, characteristic, complemented
4#16840013C212yesmaximal, complemented
5#16840010C212yesmaximal, complemented
6#16839996C212yesmaximal, complemented
7#16839993C212yesmaximal, complemented
8#16839802C211yesmaximal, characteristic, complemented
9#16839758C211yesmaximal, characteristic, complemented
10C2×#14519697C211yesmaximal, characteristic, complemented
11C61×#537C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13#14519802—24no—
14C2×#11758201C2212yes—
15C2×#11758199C2212yes—
16#14519784—24no—
17C2×#11758194C2211yescharacteristic
18C2×#11758194C2212yescomplemented
19C22×#92418C2211yescharacteristic
20C22×#92418C2212yescomplemented
21#14519773—21no—
22#14519766—21no—
23#14519751C2212yes—
24#14519751C2212yes—
25#14519745—22no—
26#14519736C2211yescharacteristic
27#14519710C2212yescomplemented
28#14519708C2212yescomplemented
29#14519701C2211yescharacteristic, complemented
30#14519701C2211yescharacteristic, complemented
31#14519698C2211yescharacteristic, complemented
32#14519698C2211yescharacteristic, complemented
33#14519697C2212yes—
34#14519697C2212yes—
35C2×#41×C61C2211yescharacteristic
36C2×#41×C61C2211yescharacteristic
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61C2212yescomplemented
39#121×C61—21no—
40#121×C61—22no—
41#121×C61C2212yescomplemented
42C2×C4⋊C4×C61C2211yescharacteristic
43C23×D61—21no—
44#41×C61—22no—
45#41×C61—22no—
46#41×C61—22no—
47#41×C61—22no—
48C2×Q8×C61D411yescharacteristic
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61—22no—
52C2×D4×C61D412yes—
53C2×D4×C61D411yescharacteristic
54C2×D4×C61C2311yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C2312yes—
58C22×C4×C61C2311yescharacteristic
59C2×C22⋊D61—22no—
60C2×C22⋊D61—22no—
61C2×D244—22no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—22no—
67C4⋊C4×C61C2312yes—
68C22⋊C4×C61—22no—
69C22⋊C4×C61—22no—
70C22⋊Dic61—21no—
71#11758201—24no—
72#11758199—24no—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77C4×Dic61—21no—
78#11758194—24no—
79#11758194D414yescomplemented
80C2×#92418—22no—
81C2×#92418—24no—
82C2×#92418C2311yescharacteristic
83C2×#92418C2311yescharacteristic
84C2×#92418C2312yes—
85C23×C61—21no—
86C23×C61C2×D412yes—
87C23×C61C2×D411yescharacteristic
88C22×D61—22no—
89C22×D61—42no—
90C22×D61—81no—
91C22×D61—81no—
92Q8×C61—22no—
93Q8×C61—21no—
94Q8×C61—21no—
95D4×C61—24no—
96D4×C61—22no—
97D4×C61—21no—
98D4×C61—21no—
99D4×C61—42no—
100D4×C61—82no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61—81no—
107C2×C4×C61C2×D412yes—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D412yes—
110C2×C4×C61#4112yes—
111C2×C4×C61C2411yescharacteristic
112C22⋊D61—82no—
113C22⋊D61—82no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116D244—22no—
117D244—22no—
118D244—42no—
119#92418—21no—
120#92418—21no—
121#92418C2×D414yes—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61#12112yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—84no—
136C4×C61—22no—
137C4×C61—41no—
138C4×C61—42no—
139C4×C61#12112yes—
140C4×C61C22×D411yescharacteristic
141C4×C61C2×#4111yescharacteristic
142Dic61—41no—
143Dic61—41no—
144#3062—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61—81no—
148C2×C61C2×#12111yescharacteristic
149C2×C61#57611yescharacteristic
150C2×C61#57711yescharacteristic
151D61—82no—
152C2×AGL(1,ℤ/8)—611no—
153C2×#131—611no—
154#537D6111yescharacteristic, complemented
155#535—611no—
156#469—612no—
157#468—612no—
158#466—612no—
159#465—612no—
160#428—611no—
161#416—611no—
162C2×#102—611no—
163C61#306211yescharacteristic, complemented, Sylow
164C2×#41C2×D6111yescharacteristic
165C2×#41C2×D6111yescharacteristic
166C22×D4—611no—
167AGL(1,ℤ/8)—1224no—
168C2×SD16—612no—
169C2×D8—612no—
170#131—1224no—
171C2×M16—611no—
172C2×M16—612no—
173C22×C8—611no—
174C22×C8—612no—
175#127—1221no—
176#124—1221no—
177C22⋊Q8—21no—
178C22⋊Q8C2×D6112yescomplemented
179#121—21no—
180#121—22no—
181#121—612no—
182#121—612no—
183#121C2×D6112yescomplemented
184#120—1222no—
185#117—611no—
186C2×C4⋊C4C2×D6111yescharacteristic
187#107—612no—
188#106—612no—
189#103—611no—
190#103—611no—
191#102—611no—
192#102—611no—
193#102—612no—
194#102—612no—
195C24—1221no—
196#41—22no—
197#41—22no—
198#41—22no—
199#41—22no—
200C2×Q8C22⋊D6111yescharacteristic
201C2×Q8C22×D6111yescharacteristic
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—612no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4C22⋊D6112yes—
211C2×D4C22⋊D6111yescharacteristic
212C2×D4C22×D6111yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4C22×D6112yes—
216C22×C4C22×D6111yescharacteristic
217SD16—1224no—
218D8—1224no—
219M16—614no—
220M16—1224no—
221C2×C8—612no—
222C2×C8—611no—
223C2×C8—611no—
224C2×C8—1224no—
225C2×C8—1222no—
226C4⋊C4—21no—
227C4⋊C4—22no—
228C4⋊C4—611no—
229C4⋊C4—611no—
230C4⋊C4C22×D6112yes—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—1221no—
234C22⋊C4—1222no—
235C22⋊C4—1222no—
236C42—1221no—
237C23—21no—
238C23—1222no—
239C23—4881no—
240C23—4881no—
241C23—2442no—
242C23C2×C22⋊D6112yes—
243C23C2×C22⋊D6111yescharacteristic
244Q8—22no—
245Q8—21no—
246Q8—21no—
247D4—24no—
248D4—21no—
249D4—21no—
250D4—22no—
251D4—42no—
252D4—82no—
253D4—1222no—
254D4—1222no—
255D4—4882no—
256D4—4882no—
257D4—2442no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—81no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4D4×D6112yes—
267C2×C4#1175822412yes—
268C2×C4C2×C22⋊D6112yes—
269C2×C4C2×C22⋊D6111yescharacteristic
270C2×C4C23×D6111yescharacteristic
271C8—614no—
272C8—1221no—
273C8—1221no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—4884no—
283C22—2442no—
284C22—2442no—
285C22—2442no—
286C22#1451974912yes—
287C22C22×C22⋊D6111yescharacteristic
288C4—22no—
289C4—41no—
290C4—42no—
291C4—2441no—
292C4—2441no—
293C4#1451974912yes—
294C4C2×D4×D6111yescharacteristic
295C4C2×#1175822411yescharacteristic
296C2—22no—
297C2—42no—
298C2—81no—
299C2—4882no—
300C2C2×#1451974911yescharacteristic
301C2#1684056511yescharacteristic
302C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#537C2
socleC22×C61C22×D4
hypercenter#537D61
hypocenterC61#3062
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C2×#14519784C2semidirect
3. #16840326C2semidirect
4. #16840013C2semidirect
5. #16840010C2semidirect
6. #16839996C2semidirect
7. #16839993C2semidirect
8. #16839802C2semidirect
9. #16839758C2semidirect
10. C2×#14519697C2semidirect
11. C61×#537C2semidirect
18. C2×#11758194C22semidirect
20. C22×#92418C22semidirect
27. #14519710C22semidirect
28. #14519708C22semidirect
29. #14519701C22semidirect
30. #14519701C22semidirect
31. #14519698C22semidirect
32. #14519698C22semidirect
38. C22⋊Q8×C61C22semidirect
41. #121×C61C22semidirect
79. #11758194D4semidirect
154. #537D61semidirect
163. C61#3062semidirect
178. C22⋊Q8C2×D61semidirect
183. #121C2×D61semidirect