Finite Group Databasebeta

← #21455428

Subgroups — #21455428

Order 7808.

500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519799C211yesmaximal, characteristic, complemented
2#16840273C212yesmaximal, complemented
3#16840020C212yesmaximal, complemented
4#16840015C212yesmaximal, complemented
5#16840008C214yesmaximal, complemented
6#16839800C211yesmaximal, characteristic, complemented
7#16839759C212yesmaximal, complemented
8C22×M16×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10#14519799—24no—
11C2×Dic244C2211yescharacteristic, complemented
12C2×#11758190C2212yescomplemented
13C2×D488C2211yescharacteristic, complemented
14#14519760—22no—
15#14519756C2214yes—
16#14519751C2214yes—
17#14519746—22no—
18C4×C22⋊D61—24no—
19#14519736C2212yes—
20#14519711C2212yescomplemented
21#14519709C2212yescomplemented
22#14519702C2214yescomplemented
23#14519699C2214yescomplemented
24C23×C4×C61C2211yescharacteristic
25C2×M16×C61—24no—
26C2×M16×C61C2212yes—
27C2×M16×C61C2212yes—
28C22×C8×C61C2211yescharacteristic
29C22×C8×C61C2211yescharacteristic
30C24×C61D411yescharacteristic
31C22×C4×C61—22no—
32C22×C4×C61—22no—
33C22×C4×C61D412yes—
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—22no—
38C2×C22⋊D61—24no—
39#11758222—24no—
40#11758222—24no—
41C2×D244C2312yes—
42C2×C4×D61—22no—
43C2×Dic122C2312yes—
44M16×C61—24no—
45M16×C61—24no—
46C2×C8×C61—22no—
47C2×C8×C61D414yescomplemented
48C2×C8×C61C2312yes—
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2311yescharacteristic
51C22⋊Dic61—22no—
52C22⋊Dic61—24no—
53#11758198—24no—
54C4⋊Dic61C2314yes—
55#11758196—24no—
56C4×Dic61—22no—
57Dic244—22no—
58D488—22no—
59#11758190—24no—
60C23×C61—22no—
61C23×C61—42no—
62C23×C61C2×D412yes—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—24no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D412yes—
72C2×C4×C61#4112yes—
73C2×C4×C61C2411yescharacteristic
74C22⋊D61—48no—
75C22⋊D61—44no—
76C2×Dic61—24no—
77C2×Dic61—22no—
78D244—22no—
79D244—22no—
80C4×D61—44no—
81Dic122—22no—
82Dic122—22no—
83C8×C61—22no—
84C8×C61C2×D412yes—
85C8×C61C2×D412yes—
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—24no—
89C22×C61—44no—
90C22×C61#12112yes—
91C22×C61C22×D411yescharacteristic
92C2×D61—42no—
93C2×D61—44no—
94C4×C61—22no—
95C4×C61#12112yes—
96C4×C61C22×D411yescharacteristic
97C4×C61C2×#4111yescharacteristic
98Dic61—42no—
99Dic61—44no—
100#3054—611nomaximal, Sylow
101C2×C61—22no—
102C2×C61—42no—
103C2×C61C2×#12111yescharacteristic
104C2×C61#57512yes—
105D61—82no—
106C2×#135—611no—
107C22×M16D6111yescharacteristic, complemented
108#525—612no—
109#470—612no—
110#469—612no—
111#468—614no—
112#427—611no—
113#416—612no—
114C61#305411yescharacteristic, complemented, Sylow
115C2×#41—612no—
116C23×C4C2×D6111yescharacteristic
117#135—1224no—
118C2×Q16—611no—
119C2×SD16—612no—
120C2×D8—611no—
121C2×M16—24no—
122C2×M16C2×D6112yes—
123C2×M16C2×D6112yes—
124C22×C8C2×D6111yescharacteristic
125C22×C8C2×D6111yescharacteristic
126#123—1222no—
127C22⋊Q8—614no—
128#121—614no—
129#120—1222no—
130C4×D4—1224no—
131#117—612no—
132#107—612no—
133#106—612no—
134#103—614no—
135#102—614no—
136C24D24411yescharacteristic
137#41—1224no—
138#41—1224no—
139C2×Q8—612no—
140C2×D4—612no—
141C2×D4—1224no—
142C2×D4—1222no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—1222no—
146C22×C4D24411yescharacteristic
147C22×C4D24412yes—
148C22×C4C22×D6112yes—
149C22×C4C22×D6111yescharacteristic
150Q16—1222no—
151SD16—1224no—
152D8—1222no—
153M16—24no—
154M16—24no—
155C2×C8—22no—
156C2×C8C22⋊D6114yescomplemented
157C2×C8C22×D6112yes—
158C2×C8C22×D6111yescharacteristic
159C2×C8C22×D6111yescharacteristic
160C4⋊C4—614no—
161C4⋊C4—1224no—
162C22⋊C4—1222no—
163C22⋊C4—1224no—
164C22⋊C4—1224no—
165C42—1222no—
166C23—22no—
167C23—42no—
168C23—1222no—
169C23C2×D24412yes—
170C23C2×D24411yescharacteristic
171Q8—1222no—
172Q8—1222no—
173D4—1222no—
174D4—1222no—
175D4—2448no—
176D4—2444no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—1224no—
182C2×C4—1222no—
183C2×C4—2444no—
184C2×C4C2×D24412yes—
185C2×C4C2×D24411yescharacteristic
186C2×C4#1175822212yes—
187C2×C4C2×C22⋊D6112yes—
188C2×C4C23×D6111yescharacteristic
189C8—22no—
190C8C2×C22⋊D6112yes—
191C8C2×C22⋊D6112yes—
192C22—22no—
193C22—22no—
194C22—24no—
195C22—44no—
196C22—2442no—
197C22—2444no—
198C22#1451975112yes—
199C22C22×D24411yescharacteristic
200C4—22no—
201C4—2442no—
202C4—2444no—
203C4#1451975112yes—
204C4C22×C22⋊D6111yescharacteristic
205C4C2×#1175822211yescharacteristic
206C2—22no—
207C2—42no—
208C2—4882no—
209C2C2×#1451975111yescharacteristic
210C2#1684056212yes—
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×M16×C61C2
socleC22×C61C22×D4
hypercenterC22×M16D61
hypocenterC61#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. #16840273C2semidirect
3. #16840020C2semidirect
4. #16840015C2semidirect
5. #16840008C2semidirect
6. #16839800C2semidirect
7. #16839759C2semidirect
8. C22×M16×C61C2semidirect
11. C2×Dic244C22semidirect
12. C2×#11758190C22semidirect
13. C2×D488C22semidirect
20. #14519711C22semidirect
21. #14519709C22semidirect
22. #14519702C22semidirect
23. #14519699C22semidirect
47. C2×C8×C61D4semidirect
107. C22×M16D61semidirect
114. C61#3054semidirect
156. C2×C8C22⋊D61semidirect