Finite Group Databasebeta

← #21457428

Subgroups — #21457428

Order 7808.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14519804C212yesmaximal, complemented
2#16840405C212yesmaximal, complemented
3#16840005C212yesmaximal, complemented
4#16839974C212yesmaximal, complemented
5#16839923C212yesmaximal, complemented
6#16839894C212yesmaximal, complemented
7C4×D488C211yesmaximal, characteristic, complemented
8#16839841C211yesmaximal, characteristic, complemented
9C61×#495C211yesmaximal, characteristic, complemented
10C2×#11758226C2212yes—
11C2×D4×D61C2212yescomplemented
12#14519804—28no—
13C2×#11758201C2212yescomplemented
14C2×D488C2211yescharacteristic
15C2×#11758199C2212yes—
16C2×#11758189C2212yescomplemented
17#14519759—22no—
18#14519753C2212yescomplemented
19#14519750—22no—
20#14519748C2212yes—
21#14519747—22no—
22C4×D244C2211yescharacteristic
23C4×D244C2212yescomplemented
24C22⋊C4×D61—22no—
25#14519711C2211yescharacteristic, complemented
26C4⋊#92418C2211yescharacteristic, complemented
27#14519701C2212yescomplemented
28#14519699C2212yescomplemented
29#14519698C2212yescomplemented
30#14519689C2212yescomplemented
31C2×Q16×C61C2211yescharacteristic, complemented
32C2×SD16×C61C2212yescomplemented
33C2×D8×C61C2211yescharacteristic
34#124×C61C2212yescomplemented
35C4×C8×C61C2211yescharacteristic, complemented
36C23×D61—22no—
37C2×Q8×C61C2312yes—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41#11758226—24no—
42#11758226—42no—
43D4×D61—24no—
44D4×D61—42no—
45C2×D244—22no—
46C2×D244D411yescharacteristic
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61C2312yes—
51Q16×C61—41no—
52SD16×C61—24no—
53D8×C61—41no—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C22⋊C4×C61—22no—
57C22⋊C4×C61—22no—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758201—24no—
61#11758199—24no—
62#11758198—22no—
63#11758198—22no—
64#11758198D412yes—
65C4⋊Dic61D411yescharacteristic
66C4⋊Dic61C2312yes—
67#11758196—22no—
68C2×#92418C2312yes—
69D488D414yescomplemented
70#11758189—24no—
71C23×C61—22no—
72C22×D61—22no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61—82no—
76C22×D61C2×D412yes—
77Q8×C61—22no—
78Q8×C61—22no—
79D4×C61—22no—
80D4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C22⋊D61—82no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89D244—22no—
90D244—41no—
91D244—44no—
92D244C2×D414yes—
93C4×D61—22no—
94C4×D61—22no—
95C4×D61—44no—
96C4×D61—82no—
97C8×C61—21no—
98C8×C61C2×D412yes—
99#92418—22no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61C22×D411yescharacteristic
104C2×D61—22no—
105C2×D61—24no—
106C2×D61—22no—
107C2×D61—22no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—88no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61C22×D411yescharacteristic
115C4×C61H(5,𝔽2)11yescharacteristic
116Dic61—22no—
117Dic61—42no—
118#3273—611nomaximal, Sylow
119C2×C61—82no—
120C2×C61D4211yescharacteristic
121C2×C61#57511yescharacteristic
122C2×C61#57611yescharacteristic
123D61—42no—
124D61—44no—
125C2×AGL(1,ℤ/8)—612no—
126#546—612no—
127#495D6111yescharacteristic, complemented
128#468—612no—
129#463—612no—
130#452—612no—
131#447—612no—
132C4×D8—611no—
133#436—611no—
134C61#327311yescharacteristic, complemented, Sylow
135C2×#41—612no—
136C22×D4—612no—
137AGL(1,ℤ/8)—1228no—
138C2×Q16C2×D6111yescharacteristic, complemented
139C2×SD16—612no—
140C2×SD16C2×D6112yescomplemented
141C2×D8—612no—
142C2×D8—611no—
143C2×D8C2×D6111yescharacteristic
144C2×M16—612no—
145#124C2×D6112yescomplemented
146#123—1222no—
147C22⋊Q8—612no—
148#121—612no—
149#121—1222no—
150#120—1222no—
151C4×D4—611no—
152C4×D4—612no—
153C2×C22⋊C4—1222no—
154#107—611no—
155C4⋊C8—611no—
156#103—612no—
157#102—612no—
158#102—612no—
159C22⋊C8—612no—
160C4×C8C2×D6111yescharacteristic, complemented
161C24—1222no—
162#41—1224no—
163#41—2442no—
164C2×Q8C22×D6112yes—
165C2×D4—611no—
166C2×D4—612no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1224no—
170C2×D4—1222no—
171C2×D4—2442no—
172C2×D4C22×D6112yes—
173C22×C4—612no—
174C22×C4—1222no—
175C22×C4—1222no—
176Q16—41no—
177SD16—24no—
178SD16—1224no—
179D8—41no—
180D8—614no—
181D8—1224no—
182M16—1224no—
183C2×C8—612no—
184C2×C8C22×D6111yescharacteristic
185C2×C8C22×D6111yescharacteristic
186C4⋊C4—611no—
187C4⋊C4—612no—
188C4⋊C4—1222no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—612no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C42C22×D6111yescharacteristic
196C23—22no—
197C23—612no—
198C23—1222no—
199C23—4882no—
200C23—2444no—
201C23—2444no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—614no—
207D4—1222no—
208D4—4882no—
209D4—2441no—
210D4—2444no—
211D4—2444no—
212C2×C4—22no—
213C2×C4—612no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—4882no—
218C2×C4—2444no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4C23×D6111yescharacteristic
222C8—21no—
223C8—1222no—
224C8D4×D6112yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—1222no—
229C22—1222no—
230C22—1222no—
231C22—1224no—
232C22—4888no—
233C22—2442no—
234C22—2442no—
235C22C2×D4×D6111yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—1222no—
240C4—2442no—
241C4C2×D4×D6111yescharacteristic
242C4#1451982211yescharacteristic
243C2—82no—
244C2—2442no—
245C2—2444no—
246C2#1684039711yescharacteristic
247C2#1684055911yescharacteristic
248C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. #16840405C2semidirect
3. #16840005C2semidirect
4. #16839974C2semidirect
5. #16839923C2semidirect
6. #16839894C2semidirect
7. C4×D488C2semidirect
8. #16839841C2semidirect
9. C61×#495C2semidirect
11. C2×D4×D61C22semidirect
13. C2×#11758201C22semidirect
16. C2×#11758189C22semidirect
18. #14519753C22semidirect
23. C4×D244C22semidirect
25. #14519711C22semidirect
26. C4⋊#92418C22semidirect
27. #14519701C22semidirect
28. #14519699C22semidirect
29. #14519698C22semidirect
30. #14519689C22semidirect
31. C2×Q16×C61C22semidirect
32. C2×SD16×C61C22semidirect
34. #124×C61C22semidirect
35. C4×C8×C61C22semidirect
69. D488D4semidirect
127. #495D61semidirect
134. C61#3273semidirect
138. C2×Q16C2×D61semidirect
140. C2×SD16C2×D61semidirect
145. #124C2×D61semidirect
160. C4×C8C2×D61semidirect