Finite Group Databasebeta

← #21456062

Subgroups — #21456062

Order 7808.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840367C211yesmaximal, characteristic, complemented
2#16840086C212yesmaximal, complemented
3#16840062C212yesmaximal, complemented
4#16839957C212yesmaximal, complemented
5#16839896C212yesmaximal, complemented
6#16839872C212yesmaximal, complemented
7C4×#11758199C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic, complemented
9C61×#518C211yesmaximal, characteristic, complemented
10C2×#11758199C2212yes—
11C2×#11758199C2212yes—
12#14519774C2211yescharacteristic, complemented
13#14519769C2211yescharacteristic, complemented
14#14519762—22no—
15#14519751C2212yes—
16#14519750—22no—
17C4×D244C2212yescomplemented
18#14519710C2212yescomplemented
19#14519708C2212yescomplemented
20C4⋊#92418C2212yescomplemented
21#14519698C2212yes—
22#14519698C2212yes—
23#14519697C2212yescomplemented
24#14519697C2212yescomplemented
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic, complemented
27C4×#92418C2211yescharacteristic, complemented
28C22×D4×C61C2211yescharacteristic
29C4×D4×C61—22no—
30C4×D4×C61C2212yes—
31C4×D4×C61C2212yes—
32#117×C61C2211yescharacteristic
33#117×C61C2211yescharacteristic
34C2×C22⋊C4×C61—22no—
35C24×C61—21no—
36C2×D4×C61—24no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×D244—22no—
44C2×D244C2312yes—
45C2×C4×D61—22no—
46C4⋊C4×C61D412yes—
47C4⋊C4×C61C2312yes—
48C22⋊C4×C61—21no—
49C22⋊C4×C61—22no—
50C22⋊C4×C61—22no—
51C22⋊C4×C61D412yes—
52C42×C61—21no—
53C42×C61C2311yescharacteristic
54C42×C61C2311yescharacteristic
55#11758199—24no—
56#11758199—24no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61—24no—
64C23×C61—22no—
65C23×C61—82no—
66C23×C61C2×D411yescharacteristic
67C22×D61—22no—
68D4×C61—24no—
69D4×C61—22no—
70D4×C61#4114yes—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—82no—
74C2×C4×C61—82no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—82no—
80C2×Dic61—22no—
81D244—22no—
82D244—22no—
83D244—82no—
84C4×D61—82no—
85#92418—22no—
86#92418—22no—
87C22×C61—21no—
88C22×C61—24no—
89C22×C61—22no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—84no—
93C22×C61C22×D411yescharacteristic
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
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—44no—
106C2×C61#52511yescharacteristic
107C2×C61#57612yes—
108D61—82no—
109#540—611no—
110#518D6111yescharacteristic, complemented
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×D4C2×D6111yescharacteristic
120C2×D8—612no—
121C2×D8—612no—
122#127—611no—
123#125—611no—
124#123—1222no—
125#121—612no—
126#121—1222no—
127C4×D4—22no—
128C4×D4—612no—
129C4×D4C2×D6112yes—
130C4×D4C2×D6112yes—
131#117C2×D6111yescharacteristic
132#117C2×D6111yescharacteristic
133C2×C22⋊C4—22no—
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—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—612no—
148C2×D4—1222no—
149C2×D4—1222no—
150C2×D4C22×D6112yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—1222no—
154C22×C4C22×D6111yescharacteristic
155D8—1224no—
156D8—1224no—
157C2×C8—612no—
158C2×C8—612no—
159C4⋊C4—612no—
160C4⋊C4—1222no—
161C4⋊C4C22⋊D6112yes—
162C4⋊C4C22×D6112yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4C22⋊D6112yes—
169C42—21no—
170C42C22×D6111yescharacteristic
171C42C22×D6111yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—1222no—
176C23C2×C22⋊D6111yescharacteristic
177D4—24no—
178D4—22no—
179D4—1222no—
180D4—1222no—
181D4—4882no—
182D4—4882no—
183D4#1175822214yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—1222no—
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—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—2442no—
203C22—2442no—
204C22—2442no—
205C22C22×C22⋊D6111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—2442no—
211C4C2×#1175822212yes—
212C2—41no—
213C2—44no—
214C2—4882no—
215C2#1684027311yescharacteristic
216C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#518C2
socleC22×C61C22×D4
hypercenter#518D61
hypocenterC61#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840086C2semidirect
3. #16840062C2semidirect
4. #16839957C2semidirect
5. #16839896C2semidirect
6. #16839872C2semidirect
7. C4×#11758199C2semidirect
8. #16839823C2semidirect
9. C61×#518C2semidirect
12. #14519774C22semidirect
13. #14519769C22semidirect
17. C4×D244C22semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. C4⋊#92418C22semidirect
23. #14519697C22semidirect
24. #14519697C22semidirect
26. #14519688C22semidirect
27. C4×#92418C22semidirect
110. #518D61semidirect
118. C61#3122semidirect