Finite Group Databasebeta

← #21445736

Subgroups — #21445736

Order 7808.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#11758222C211yesmaximal, characteristic
2C2×#14519691C214yesmaximal, complemented
3#16839625C211yesmaximal, characteristic, complemented
4C61×#381C211yesmaximal, characteristic, complemented
5C2×#11758222—22no—
6C2×#11758222—22no—
7C2×#11758222—28no—
8C22×Dic122C411yescharacteristic, complemented
9C22×D244C411yescharacteristic, complemented
10C22×C22⋊D61C2212yes—
11C22×C4×D61C412yescomplemented
12C2×C22⋊Dic61C2212yes—
13#14519691—28no—
14#14519684—22no—
15C23×C4×C61C2211yescharacteristic
16C2×C22⋊C4×C61C2212yes—
17#95×C61—22no—
18C24×C61C2311yescharacteristic
19C23×D61C2×C412yes—
20C22×C4×C61—24no—
21C22×C4×C61—22no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D412yes—
25C22×C4×C61D412yes—
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—24no—
29C2×C22⋊D61D418yes—
30C22×Dic61—22no—
31C22×Dic61C2×C412yes—
32#11758222—216no—
33#11758222—216no—
34C2×D244—24no—
35C2×D244—22no—
36C2×C4×D61—24no—
37C2×C4×D61—24no—
38C2×C4×D61—24no—
39C2×Dic122—22no—
40C2×Dic122—24no—
41C22⋊C4×C61—24no—
42C22⋊Dic61—24no—
43C23×C61—42no—
44C23×C61C22×C411yescharacteristic
45C23×C61C2×D411yescharacteristic
46C23×C61C2×D411yescharacteristic
47C23×C61C2×D414yes—
48C22×D61—22no—
49C22×D61—22no—
50C22×D61—44no—
51C22×D61C22⋊C414yes—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—24no—
55C2×C4×C61—24no—
56C2×C4×C61—44no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C412yes—
59C2×C4×C61C22⋊C412yes—
60C22⋊D61—28no—
61C22⋊D61—28no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61—44no—
65C2×Dic61—42no—
66C2×Dic61C22⋊C414yes—
67D244—28no—
68C4×D61—216no—
69Dic122—28no—
70C22×C61—22no—
71C22×C61—22no—
72C22×C61—22no—
73C22×C61—44no—
74C22×C61C2×C22⋊C412yes—
75C22×C61C2×C22⋊C411yescharacteristic
76C22×C61#12012yes—
77C22×C61#12012yes—
78C2×D61—24no—
79C2×D61—44no—
80C2×D61—44no—
81C2×D61—44no—
82C4×C61—22no—
83C4×C61—22no—
84C4×C61—82no—
85Dic61—24no—
86Dic61—82no—
87#1782—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61—22no—
90C2×C61—22no—
91C2×C61#37911yescharacteristic
92C2×C61#41012yes—
93D61—44no—
94C22×#41—611no—
95C2×#99—614no—
96#381—611no—
97#381D6111yescharacteristic, complemented
98C61#178211yescharacteristic, complemented, Sylow
99C2×#41—1228no—
100C2×#41—1222no—
101C2×#41—1222no—
102C22×Q8—611no—
103C22×D4—612no—
104C22×D4—611no—
105C23×C4—612no—
106C23×C4C2×D6111yescharacteristic
107C2×C22⋊C4—612no—
108C2×C22⋊C4C2×D6112yes—
109#99—1228no—
110#95—22no—
111#95—1222no—
112C24—612no—
113C24C22×D6111yescharacteristic
114#41—12216no—
115#41—12216no—
116C2×Q8—1224no—
117C2×Q8—1222no—
118C2×D4—618no—
119C2×D4—1224no—
120C2×D4—1222no—
121C2×D4—1224no—
122C2×D4—1222no—
123C2×D4—1222no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—612no—
127C22×C4—1224no—
128C22×C4—1224no—
129C22×C4—1224no—
130C22×C4—1222no—
131C22×C4C4×D6111yescharacteristic
132C22×C4C4×D6111yescharacteristic
133C22×C4D24412yes—
134C22×C4C22⋊D6112yes—
135C22⋊C4—24no—
136C22⋊C4—1224no—
137C23—42no—
138C23—614no—
139C23—1222no—
140C23—1222no—
141C23—2444no—
142C23C2×C4×D6111yescharacteristic
143C23C2×D24411yescharacteristic
144C23D4×D6114yes—
145C23C2×C22⋊D6111yescharacteristic
146Q8—1228no—
147D4—1228no—
148D4—1228no—
149D4—1228no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—614no—
157C2×C4—12216no—
158C2×C4—1222no—
159C2×C4—1222no—
160C2×C4—2444no—
161C2×C4—2442no—
162C2×C4#1175819812yes—
163C2×C4#1175819812yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—1224no—
169C22—2444no—
170C22—2444no—
171C22—2444no—
172C22C22⋊C4×D6112yes—
173C22C2×#1175819811yescharacteristic
174C22#1451974512yes—
175C22#1451974712yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—1224no—
180C4—4882no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—2444no—
185C2#1683961711yescharacteristic
186C2#1683973512yes—
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC61×#381C2
socleC22×C61C2×C22⋊C4
hypercenter#381D61
hypocenterC61#1782
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#14519691C2semidirect
3. #16839625C2semidirect
4. C61×#381C2semidirect
8. C22×Dic122C4semidirect
9. C22×D244C4semidirect
11. C22×C4×D61C4semidirect
97. #381D61semidirect
98. C61#1782semidirect