Finite Group Databasebeta

← #21454702

Subgroups — #21454702

Order 7808.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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
2#16840243C212yesmaximal, complemented
3#16839873C212yesmaximal, complemented
4#16839868C212yesmaximal, complemented
5#16839849C214yesmaximal, complemented
6#16839761C212yesmaximal, complemented
7#16839717C211yesmaximal, characteristic, complemented
8C2×#106×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10#14519799C418yescomplemented
11C2×Dic244C2211yescharacteristic
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519742C2214yes—
16#14519739C2214yes—
17C4×C22⋊D61—24no—
18#14519736C2211yescharacteristic
19#14519735—22no—
20C4⋊C4×D61—22no—
21#14519700C2214yes—
22#14519697C2214yes—
23#14519687C2212yes—
24C8×Dic61C2212yes—
25C22×C8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2212yes—
27#106×C61C2212yes—
28#106×C61C2212yes—
29C22×C4×C61—22no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—22no—
32#11758222—24no—
33#11758222C2×C418yescomplemented
34C2×D244C2312yes—
35C2×C4×D61—22no—
36C2×C4×D61—24no—
37C2×Dic122C2312yes—
38C2×C8×C61C2×C414yescomplemented
39C2×C8×C61C2311yescharacteristic
40C2×C8×C61C2311yescharacteristic
41C4⋊C4×C61—22no—
42C4⋊C4×C61C2314yes—
43C22⋊Dic61D412yes—
44#11758198—24no—
45C4⋊Dic61D412yes—
46#11758196—24no—
47C4×Dic61—24no—
48C4×Dic61C2312yes—
49#11758194—22no—
50C2×#92418C2312yes—
51Dic244C2×C414yescomplemented
52D488C2×C414yescomplemented
53#11758190C2×C418yescomplemented
54C23×C61C2×D411yescharacteristic
55C22×D61—22no—
56C2×C4×C61—24no—
57C2×C4×C61—82no—
58C2×C4×C61C22×C412yes—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61#4112yes—
61C2×C4×C61C2411yescharacteristic
62C22⋊D61—28no—
63C2×Dic61—22no—
64C2×Dic61C2×D414yes—
65D244—22no—
66D244C22×C414yes—
67C4×D61—28no—
68C4×D61—84no—
69Dic122—22no—
70Dic122C22×C414yes—
71C8×C61C22×C412yes—
72C8×C61C22×C412yes—
73#92418—22no—
74C22×C61—22no—
75C22×C61C4×D412yes—
76C22×C61C22×D411yescharacteristic
77C2×D61—24no—
78C2×D61—42no—
79C2×D61—42no—
80C4×C61—44no—
81C4×C61C4×D412yes—
82C4×C61C23×C411yescharacteristic
83C4×C61C2×#4111yescharacteristic
84Dic61—24no—
85Dic61—24no—
86#2952—611nomaximal, Sylow
87C2×C61—22no—
88C2×C61C2×C4×D411yescharacteristic
89C2×C61#57712yes—
90D61—44no—
91C2×#135—611no—
92#520—612no—
93#442—612no—
94#441—612no—
95C4×SD16—614no—
96C2×#106D6111yescharacteristic, complemented
97#417—612no—
98#405—611no—
99C61#295211yescharacteristic, complemented, Sylow
100C2×#41—612no—
101#135—618no—
102C2×Q16—611no—
103C2×SD16—612no—
104C2×D8—611no—
105C2×M16—611no—
106C22×C8C2×D6111yescharacteristic
107C4×Q8—614no—
108C4×D4—614no—
109C4×D4—1224no—
110#117—611no—
111#117—1222no—
112C2×C4⋊C4—1222no—
113C2×C4⋊C4C2×D6112yes—
114#106C2×D6112yes—
115#106C2×D6112yes—
116#103—614no—
117#102—614no—
118#97—612no—
119C4×C8—612no—
120#41—618no—
121#41—1224no—
122C2×Q8—612no—
123C2×D4—612no—
124C2×D4—1222no—
125C22×C4—22no—
126C22×C4—1224no—
127C22×C4—1222no—
128C22×C4C22×D6111yescharacteristic
129Q16—614no—
130SD16—618no—
131D8—614no—
132M16—1222no—
133C2×C8—612no—
134C2×C8C4×D6114yescomplemented
135C2×C8C22×D6111yescharacteristic
136C2×C8C22×D6111yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—612no—
139C4⋊C4—1224no—
140C4⋊C4C22×D6114yes—
141C22⋊C4—612no—
142C22⋊C4—1224no—
143C42—612no—
144C42—1224no—
145C23—1222no—
146C23D4×D6111yescharacteristic
147Q8—614no—
148Q8—1222no—
149D4—614no—
150D4—1228no—
151D4—1222no—
152C2×C4—24no—
153C2×C4—82no—
154C2×C4—614no—
155C2×C4—1222no—
156C2×C4—1228no—
157C2×C4—4884no—
158C2×C4C2×C4×D6112yes—
159C2×C4D4×D6111yescharacteristic
160C2×C4#1175822612yes—
161C2×C4C23×D6111yescharacteristic
162C8—1222no—
163C8C2×C4×D6112yes—
164C8C2×C4×D6112yes—
165C22—22no—
166C22—1224no—
167C22—2442no—
168C22—2442no—
169C22#1451973912yes—
170C22C2×D4×D6111yescharacteristic
171C4—44no—
172C4—1224no—
173C4—1224no—
174C4#1451973912yes—
175C4C22×C4×D6111yescharacteristic
176C4C2×#1175822611yescharacteristic
177C2—22no—
178C2—2444no—
179C2C2×#1451973911yescharacteristic
180C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC2×#106×C61C2
socleC22×C61C22×D4
hypercenterC2×#106D61
hypocenterC61#2952
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #16840243C2semidirect
3. #16839873C2semidirect
4. #16839868C2semidirect
5. #16839849C2semidirect
6. #16839761C2semidirect
7. #16839717C2semidirect
8. C2×#106×C61C2semidirect
10. #14519799C4semidirect
33. #11758222C2×C4semidirect
38. C2×C8×C61C2×C4semidirect
51. Dic244C2×C4semidirect
52. D488C2×C4semidirect
53. #11758190C2×C4semidirect
96. C2×#106D61semidirect
99. C61#2952semidirect
134. C2×C8C4×D61semidirect