Finite Group Databasebeta

← #21456306

Subgroups — #21456306

Order 7808.

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

normal subgroups only

This group has 596 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×#14519802C212yesmaximal, complemented
2C22×D488C211yesmaximal, characteristic, complemented
3#16840326C212yesmaximal, complemented
4#16840148C214yesmaximal, complemented
5#16840147C212yesmaximal, complemented
6#16840137C212yesmaximal, complemented
7#16839717C211yesmaximal, characteristic, complemented
8C2×#135×C61C211yesmaximal, characteristic, complemented
9C22×D244C2212yes—
10#14519802—28no—
11C2×#11758201C2214yescomplemented
12C2×D488—24no—
13C2×D488C2212yes—
14C2×D488C2212yes—
15C2×#11758199C2214yescomplemented
16C2×#11758194C2211yescharacteristic
17#14519773C2214yescomplemented
18#14519766C2214yescomplemented
19#14519751—24no—
20#14519745—24no—
21#14519736C2211yescharacteristic
22#14519687C2212yescomplemented
23C8×Dic61C2212yescomplemented
24C2×#41×C61C2212yes—
25#135×C61—24no—
26C2×Q16×C61C2211yescharacteristic, complemented
27C2×SD16×C61C2212yescomplemented
28C2×D8×C61C2211yescharacteristic, complemented
29C22×C8×C61C2211yescharacteristic
30C23×D61—22no—
31#41×C61—24no—
32#41×C61—24no—
33C2×Q8×C61C2312yes—
34C2×D4×C61—22no—
35C2×D4×C61C2312yes—
36C22×C4×C61—22no—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—28no—
39C2×D244—24no—
40C2×D244—24no—
41C2×D244—22no—
42C2×D244C2314yes—
43Q16×C61—22no—
44SD16×C61—24no—
45D8×C61—22no—
46C2×C8×C61D414yescomplemented
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C22⋊Dic61D412yes—
50#11758201—28no—
51#11758199—28no—
52#11758198—28no—
53C4⋊Dic61D412yes—
54C4×Dic61C2312yes—
55#11758194D414yescomplemented
56C2×#92418C2312yes—
57D488—24no—
58D488—24no—
59C23×C61—22no—
60C23×C61C2×D411yescharacteristic
61C22×D61—24no—
62C22×D61—44no—
63C22×D61—84no—
64Q8×C61—22no—
65Q8×C61—22no—
66D4×C61—22no—
67D4×C61—22no—
68D4×C61—44no—
69C2×C4×C61—22no—
70C2×C4×C61—44no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2411yescharacteristic
75C22⋊D61—88no—
76C2×Dic61C2×D414yes—
77D244—24no—
78D244—24no—
79D244—44no—
80C8×C61C2×D412yes—
81C8×C61C2×D412yes—
82#92418C2×D414yes—
83C22×C61—22no—
84C22×C61—42no—
85C22×C61—44no—
86C22×C61#12712yes—
87C22×C61C22×D411yescharacteristic
88C2×D61—44no—
89C2×D61—48no—
90C2×D61—88no—
91C4×C61—42no—
92C4×C61#12712yes—
93C4×C61C22×D411yescharacteristic
94C4×C61C22×D411yescharacteristic
95Dic61—24no—
96#3155—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61—82no—
99C2×C61C2×#12711yescharacteristic
100C2×C61#57612yes—
101D61—84no—
102C2×AGL(1,ℤ/8)—612no—
103C2×#135D6111yescharacteristic, complemented
104C22×D8—611no—
105#535—612no—
106#496—614no—
107#495—612no—
108#493—612no—
109#405—611no—
110C61#315511yescharacteristic, complemented, Sylow
111C2×#41C2×D6112yes—
112C22×D4—612no—
113AGL(1,ℤ/8)—1228no—
114#135—24no—
115C2×Q16C2×D6111yescharacteristic, complemented
116C2×SD16—614no—
117C2×SD16C2×D6112yescomplemented
118C2×D8—614no—
119C2×D8—612no—
120C2×D8—612no—
121C2×D8—1224no—
122C2×D8C2×D6111yescharacteristic, complemented
123C2×M16—611no—
124C22×C8C2×D6111yescharacteristic
125#127—614no—
126#124—614no—
127#121—1224no—
128#120—1224no—
129#117—611no—
130#97—612no—
131C4×C8—612no—
132C24—1222no—
133#41—24no—
134#41—24no—
135C2×Q8C22×D6112yes—
136C2×D4—22no—
137C2×D4—614no—
138C2×D4—1228no—
139C2×D4—1224no—
140C2×D4—1222no—
141C2×D4—1224no—
142C2×D4C22×D6112yes—
143C22×C4—22no—
144C22×C4C22×D6111yescharacteristic
145Q16—22no—
146SD16—24no—
147SD16—1228no—
148D8—22no—
149D8—1228no—
150D8—1224no—
151D8—1224no—
152M16—614no—
153C2×C8—612no—
154C2×C8C22⋊D6114yescomplemented
155C2×C8C22×D6111yescharacteristic
156C2×C8C22×D6111yescharacteristic
157C4⋊C4—612no—
158C22⋊C4—612no—
159C22⋊C4—1228no—
160C42—612no—
161C23—22no—
162C23—1224no—
163C23—4884no—
164C23—2444no—
165C23D4×D6111yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—1224no—
172D4—1224no—
173D4—4888no—
174D4—2444no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—614no—
178C2×C4D4×D6112yes—
179C2×C4D4×D6111yescharacteristic
180C2×C4C2×C22⋊D6112yes—
181C2×C4C23×D6111yescharacteristic
182C8—614no—
183C8C2×C22⋊D6112yes—
184C8C2×C22⋊D6112yes—
185C22—22no—
186C22—42no—
187C22—44no—
188C22—4888no—
189C22—2444no—
190C22—2448no—
191C22#1451977312yes—
192C22C2×D4×D6111yescharacteristic
193C4—42no—
194C4—1224no—
195C4#1451977312yes—
196C4C2×D4×D6111yescharacteristic
197C4C22×C22⋊D6111yescharacteristic
198C2—22no—
199C2—82no—
200C2—4884no—
201C2C2×#1451977311yescharacteristic
202C2#1684056412yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3155
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C22×D488C2semidirect
3. #16840326C2semidirect
4. #16840148C2semidirect
5. #16840147C2semidirect
6. #16840137C2semidirect
7. #16839717C2semidirect
8. C2×#135×C61C2semidirect
11. C2×#11758201C22semidirect
15. C2×#11758199C22semidirect
17. #14519773C22semidirect
18. #14519766C22semidirect
22. #14519687C22semidirect
23. C8×Dic61C22semidirect
26. C2×Q16×C61C22semidirect
27. C2×SD16×C61C22semidirect
28. C2×D8×C61C22semidirect
46. C2×C8×C61D4semidirect
55. #11758194D4semidirect
103. C2×#135D61semidirect
110. C61#3155semidirect
115. C2×Q16C2×D61semidirect
117. C2×SD16C2×D61semidirect
122. C2×D8C2×D61semidirect
154. C2×C8C22⋊D61semidirect