Finite Group Databasebeta

← #21456057

Subgroups — #21456057

Order 7808.

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

normal subgroups only

This group has 418 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
1#16840236C211yesmaximal, characteristic, complemented
2#16840083C212yesmaximal, complemented
3#16840059C212yesmaximal, complemented
4#16839954C212yesmaximal, complemented
5#16839895C212yesmaximal, complemented
6#16839872C212yesmaximal, complemented
7C4×#11758199C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic, complemented
9C61×#540C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×#11758199C2212yes—
12C2×#11758199C2212yes—
13C4×D244C2212yes—
14C4×D244C2212yes—
15#14519739—22no—
16#14519736C2211yescharacteristic
17C22⋊C4×D61—22no—
18#14519710C2212yescomplemented
19#14519708C2212yescomplemented
20C4⋊#92418C2212yescomplemented
21#14519698C2212yescomplemented
22#14519698C2212yescomplemented
23#14519697C2212yes—
24#14519697C2212yes—
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic, complemented
27C4×#92418C2211yescharacteristic, complemented
28#127×C61C2211yescharacteristic, complemented
29#125×C61C2211yescharacteristic, complemented
30#123×C61—22no—
31#121×C61—22no—
32#121×C61C2212yes—
33C4×D4×C61C2212yescomplemented
34#117×C61C2211yescharacteristic
35C23×D61—21no—
36C2×D4×C61—22no—
37C2×D4×C61—22no—
38C2×D4×C61C2312yes—
39C22×C4×C61—22no—
40C22×C4×C61C2311yescharacteristic
41C2×D244—21no—
42C2×D244—24no—
43C2×D244C2312yes—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61D412yes—
48C4⋊C4×C61C2312yes—
49C22⋊C4×C61—22no—
50C22⋊C4×C61—22no—
51C22⋊C4×C61D412yes—
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—21no—
55#11758199—24no—
56#11758199—24no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61C2312yes—
60C4×Dic61—21no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61—22no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C22×D61—24no—
67C22×D61—82no—
68D4×C61—22no—
69D4×C61—22no—
70D4×C61—82no—
71D4×C61—82no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—82no—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2411yescharacteristic
79C2×Dic61—22no—
80D244—24no—
81D244—22no—
82D244#4114yes—
83C4×D61—82no—
84C4×D61—82no—
85#92418—22no—
86#92418—22no—
87C22×C61—21no—
88C22×C61—22no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61C22×D411yescharacteristic
93C2×D61—24no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—84no—
97C4×C61—21no—
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—42no—
101C4×C61C2×#4112yes—
102Dic61—42no—
103#3122—611nomaximal, Sylow
104C2×C61—41no—
105C2×C61—82no—
106C2×C61#52511yescharacteristic
107C2×C61#57612yes—
108D61—44no—
109#540D6111yescharacteristic, complemented
110#518—611no—
111#482—612no—
112#478—612no—
113#459—612no—
114#447—612no—
115#442—612no—
116C4×D8—612no—
117#433—611no—
118C61#312211yescharacteristic, complemented, Sylow
119C22×D4—611no—
120C2×D8—612no—
121C2×D8—612no—
122#127C2×D6111yescharacteristic, complemented
123#125C2×D6111yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D6112yes—
127C4×D4—612no—
128C4×D4—612no—
129C4×D4—1222no—
130C4×D4C2×D6112yescomplemented
131#117—611no—
132#117C2×D6111yescharacteristic
133C2×C22⋊C4—1222no—
134#107—612no—
135#106—612no—
136C4⋊C8—612no—
137#102—612no—
138#102—612no—
139#102—612no—
140#102—612no—
141C22⋊C8—612no—
142#97—611no—
143C4×C8—611no—
144C24—1221no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—612no—
148C2×D4—1224no—
149C2×D4—1221no—
150C2×D4C22×D6112yes—
151C22×C4—22no—
152C22×C4—1222no—
153C22×C4—1222no—
154C22×C4C22×D6111yescharacteristic
155D8—1224no—
156D8—1224no—
157C2×C8—612no—
158C2×C8—612no—
159C4⋊C4—22no—
160C4⋊C4—612no—
161C4⋊C4C22⋊D6112yes—
162C4⋊C4C22×D6112yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—1221no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4C22⋊D6112yes—
169C42—1221no—
170C42C22×D6111yescharacteristic
171C42C22×D6111yescharacteristic
172C23—22no—
173C23—1224no—
174C23—1222no—
175C23—4882no—
176C23C2×C22⋊D6111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—614no—
182D4—1224no—
183D4—1222no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—1222no—
188C2×C4—4882no—
189C2×C4—4882no—
190C2×C4C2×C22⋊D6111yescharacteristic
191C2×C4C2×C22⋊D6112yes—
192C2×C4C2×C22⋊D6112yes—
193C2×C4C23×D6111yescharacteristic
194C8—1222no—
195C8—1222no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—1224no—
202C22—4884no—
203C22—2442no—
204C22—2442no—
205C22C22×C22⋊D6111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—2442no—
211C4#41×D6112yes—
212C2—41no—
213C2—82no—
214C2—2444no—
215C2#1684026911yescharacteristic
216C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#540C2
socleC22×C61C22×D4
hypercenter#540D61
hypocenterC61#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16840236C2semidirect
2. #16840083C2semidirect
3. #16840059C2semidirect
4. #16839954C2semidirect
5. #16839895C2semidirect
6. #16839872C2semidirect
7. C4×#11758199C2semidirect
8. #16839823C2semidirect
9. C61×#540C2semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. C4⋊#92418C22semidirect
21. #14519698C22semidirect
22. #14519698C22semidirect
26. #14519688C22semidirect
27. C4×#92418C22semidirect
28. #127×C61C22semidirect
29. #125×C61C22semidirect
33. C4×D4×C61C22semidirect
109. #540D61semidirect
118. C61#3122semidirect
122. #127C2×D61semidirect
123. #125C2×D61semidirect
130. C4×D4C2×D61semidirect