Finite Group Databasebeta

← #21458952

Subgroups — #21458952

Order 7808.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#135×D61C212yesmaximal, complemented
2#16840204C212yesmaximal, complemented
3#16840201C212yesmaximal, complemented
4#16840199C212yesmaximal, complemented
5#16840196C212yesmaximal, complemented
6#16840194C211yesmaximal, characteristic, complemented
7#16840192C212yesmaximal, complemented
8C2×#14519716C211yesmaximal, characteristic, complemented
9C61×#508C211yesmaximal, characteristic, complemented
10#41×D61—22no—
11#14519800C2212yes—
12#14519799C2212yescomplemented
13#14519798—22no—
14#14519797—22no—
15#14519796C2212yes—
16Q16×D61C2212yescomplemented
17SD16×D61—22no—
18D8×D61C2212yescomplemented
19C2×C8×D61C2211yescharacteristic
20Dic488C2211yescharacteristic, complemented
21#14519723C2212yescomplemented
22#14519722C2212yescomplemented
23#14519721C2212yescomplemented
24#14519720C2212yescomplemented
25D976C2211yescharacteristic, complemented
26#14519718C2212yescomplemented
27#14519716C2212yescomplemented
28#14519716C2212yescomplemented
29C2×#11758185C2211yescharacteristic, complemented
30#135×C61C2212yescomplemented
31Q32×C61C2211yescharacteristic, complemented
32SD32×C61C2212yescomplemented
33D16×C61C2211yescharacteristic, complemented
34C2×C16×C61C2211yescharacteristic, complemented
35#41×C61—22no—
36#11758226—22no—
37Q8×D61—22no—
38#11758224—22no—
39#11758224—42no—
40D4×D61—22no—
41D4×D61—42no—
42#11758222—22no—
43#11758222—42no—
44C2×C4×D61—42no—
45C2×C4×D61D411yescharacteristic
46Q16×C61C2312yes—
47SD16×C61—22no—
48D8×C61C2312yes—
49C2×C8×C61C2311yescharacteristic
50#11758202—22no—
51#11758201—22no—
52#11758200—22no—
53#11758199—22no—
54C2×#92418D411yescharacteristic
55Dic244C2312yes—
56D488C2312yes—
57#11758190—22no—
58C8×D61D412yes—
59C8×D61C2312yes—
60C16×C61C2311yescharacteristic
61C16×C61C2311yescharacteristic
62#11758185C2312yes—
63C22×D61—42no—
64C22×D61D811yescharacteristic
65Q8×C61—22no—
66D4×C61—22no—
67D4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61C2×D411yescharacteristic
70C22⋊D61—42no—
71C22⋊D61—42no—
72C22⋊D61—42no—
73C2×Dic61—42no—
74C2×Dic61D811yescharacteristic
75D244—22no—
76D244—42no—
77C4×D61—42no—
78C4×D61—42no—
79C4×D61—42no—
80C4×D61D812yes—
81C4×D61C2×D412yes—
82Dic122—22no—
83Dic122—42no—
84C8×C61C2×D411yescharacteristic
85C8×C61C2411yescharacteristic
86#92418C2×D412yes—
87C22×C61—42no—
88C22×C61C2×D811yescharacteristic
89C2×D61—41no—
90C2×D61—42no—
91C2×D61—84no—
92C2×D61C2×D812yes—
93C4×C61—42no—
94C4×C61C2×D811yescharacteristic
95C4×C61C22×D411yescharacteristic
96Dic61—42no—
97Dic61C2×D812yes—
98#3414—611nomaximal, Sylow
99C2×C61—21no—
100C2×C61—82no—
101C2×C61C22×D811yescharacteristic
102D61—22no—
103D61—82no—
104C2×#135—612no—
105#510—612no—
106#510—612no—
107#509—612no—
108#509—612no—
109#508—612no—
110#508—611no—
111#508D6111yescharacteristic, complemented
112C2×M32—611no—
113C61#341411yescharacteristic, complemented, Sylow
114C2×#41—1222no—
115#135—612no—
116#135—612no—
117#135—612no—
118#135—1222no—
119#135—1222no—
120#135C2×D6112yescomplemented
121C2×Q16—612no—
122C2×SD16—1222no—
123C2×D8—612no—
124C22×C8—611no—
125Q32—612no—
126Q32—611no—
127Q32C2×D6111yescharacteristic, complemented
128SD32—612no—
129SD32—612no—
130SD32—612no—
131SD32C2×D6112yescomplemented
132D16—612no—
133D16—611no—
134D16C2×D6111yescharacteristic, complemented
135M32—612no—
136M32—612no—
137C2×C16—611no—
138C2×C16C2×D6111yescharacteristic, complemented
139#41—22no—
140#41—1222no—
141#41—1222no—
142#41—1222no—
143#41—2442no—
144#41—2442no—
145C2×Q8—1222no—
146C2×D4—1222no—
147C2×D4—2442no—
148C22×C4—611no—
149C22×C4—2442no—
150Q16—612no—
151Q16—1222no—
152Q16C22×D6112yes—
153SD16—22no—
154SD16—1222no—
155SD16—1222no—
156SD16—1222no—
157D8—612no—
158D8—1222no—
159D8C22×D6112yes—
160C2×C8—611no—
161C2×C8—612no—
162C2×C8—612no—
163C2×C8C22×D6111yescharacteristic
164C16—612no—
165C16C22×D6111yescharacteristic
166C16C22×D6111yescharacteristic
167C23—611no—
168C23—2442no—
169Q8—22no—
170Q8—1222no—
171Q8—2442no—
172D4—22no—
173D4—42no—
174D4—1222no—
175D4—2442no—
176D4—2442no—
177D4—2442no—
178D4—2442no—
179C2×C4—42no—
180C2×C4—611no—
181C2×C4—612no—
182C2×C4—612no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4D4×D6111yescharacteristic
188C8—612no—
189C8D4×D6111yescharacteristic
190C8C23×D6111yescharacteristic
191C22—42no—
192C22—612no—
193C22—4884no—
194C22—2441no—
195C22—2442no—
196C22D8×D6111yescharacteristic
197C4—42no—
198C4—612no—
199C4—2442no—
200C4D8×D6111yescharacteristic
201C4C2×D4×D6111yescharacteristic
202C2—21no—
203C2—82no—
204C2—1222no—
205C2—4882no—
206C2C2×D8×D6111yescharacteristic
subgroupG/H
centerC4D8×D61
commutatorC8×C61C24
FrattiniC8C23×D61
FittingC61×#508C2
socleC2×C61C22×D8
hypercenter#508D61
hypocenterC61#3414
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D61C2semidirect
2. #16840204C2semidirect
3. #16840201C2semidirect
4. #16840199C2semidirect
5. #16840196C2semidirect
6. #16840194C2semidirect
7. #16840192C2semidirect
8. C2×#14519716C2semidirect
9. C61×#508C2semidirect
12. #14519799C22semidirect
16. Q16×D61C22semidirect
18. D8×D61C22semidirect
20. Dic488C22semidirect
21. #14519723C22semidirect
22. #14519722C22semidirect
23. #14519721C22semidirect
24. #14519720C22semidirect
25. D976C22semidirect
26. #14519718C22semidirect
27. #14519716C22semidirect
28. #14519716C22semidirect
29. C2×#11758185C22semidirect
30. #135×C61C22semidirect
31. Q32×C61C22semidirect
32. SD32×C61C22semidirect
33. D16×C61C22semidirect
34. C2×C16×C61C22semidirect
111. #508D61semidirect
113. C61#3414semidirect
120. #135C2×D61semidirect
127. Q32C2×D61semidirect
131. SD32C2×D61semidirect
134. D16C2×D61semidirect
138. C2×C16C2×D61semidirect