Finite Group Databasebeta

← #21446366

Subgroups — #21446366

Order 7808.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840326C211yesmaximal, characteristic
2#16839746C211yesmaximal, characteristic, complemented
3C2×#14519693C212yesmaximal, complemented
4#16839534C212yesmaximal, complemented
5C61×#568C211yesmaximal, characteristic, complemented
6C22×D244C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519773—21no—
9#14519766—21no—
10#14519751—22no—
11#14519745C414yes—
12#14519736C2211yescharacteristic
13#14519696—21no—
14#14519694—21no—
15#14519693—24no—
16C2×#41×C61C2211yescharacteristic
17#131×C61—24no—
18C2×M16×C61—22no—
19C2×M16×C61C2212yes—
20C23×D61C2×C412yes—
21#41×C61—22no—
22#41×C61—22no—
23C2×Q8×C61D411yescharacteristic
24C2×D4×C61C2×C412yes—
25C2×D4×C61D411yescharacteristic
26C22×C4×C61D412yes—
27C22×C4×C61C2311yescharacteristic
28C2×C22⋊D61—24no—
29C2×D244—22no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—22no—
33M16×C61—24no—
34M16×C61—22no—
35M16×C61D414yescomplemented
36C2×C8×C61—24no—
37C2×C8×C61—22no—
38C22⋊Dic61C2×C412yes—
39#11758198—24no—
40C4⋊Dic61—21no—
41C4×Dic61—21no—
42#11758194—22no—
43#11758194—22no—
44C2×#92418—22no—
45C23×C61C22⋊C412yes—
46C23×C61C22×C411yescharacteristic
47C22×D61—22no—
48C22×D61—24no—
49C22×D61—82no—
50Q8×C61—22no—
51D4×C61—24no—
52D4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61C22⋊C412yes—
56C2×C4×C61C2×D412yes—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61#4112yes—
60C22⋊D61—84no—
61C2×Dic61—22no—
62D244—41no—
63D244—42no—
64D244—41no—
65C8×C61—24no—
66#92418—42no—
67C22×C61—22no—
68C22×C61—41no—
69C22×C61—42no—
70C22×C61C2×C22⋊C411yescharacteristic
71C22×C61C4×D412yes—
72C2×D61—44no—
73C2×D61—42no—
74C2×D61—84no—
75C4×C61—22no—
76C4×C61#12011yescharacteristic
77C4×C61#12112yes—
78C4×C61#12311yescharacteristic
79Dic61—42no—
80#1914—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—22no—
83C2×C61—42no—
84C2×C61#38611yescharacteristic
85D61—82no—
86#568D6111yescharacteristic, complemented
87#535—611no—
88#413—611no—
89C2×#100—612no—
90#344—612no—
91C61#191411yescharacteristic, complemented, Sylow
92C2×#41C2×D6111yescharacteristic
93C22×D4—611no—
94#131—24no—
95C2×M16—22no—
96C2×M16—612no—
97C2×M16C2×D6112yes—
98#127—1221no—
99#124—1221no—
100#121—1222no—
101#120—614no—
102#117—611no—
103#101—1221no—
104#100—1221no—
105#100—1224no—
106C24—612no—
107#41—22no—
108#41—22no—
109C2×Q8D24411yescharacteristic
110C2×D4—1224no—
111C2×D4—1221no—
112C2×D4—1222no—
113C2×D4—1222no—
114C2×D4—1221no—
115C2×D4C4×D6112yes—
116C2×D4D24411yescharacteristic
117C22×C4C22⋊D6112yes—
118C22×C4C22×D6111yescharacteristic
119M16—24no—
120M16—22no—
121M16—1222no—
122M16—1222no—
123M16C22⋊D6114yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—1222no—
127C4⋊C4—1221no—
128C22⋊C4—612no—
129C22⋊C4—1224no—
130C42—1221no—
131C23—1224no—
132C23—1222no—
133C23—4882no—
134C23#1175819812yes—
135C23C2×C4×D6111yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—4884no—
140D4—2441no—
141D4—2442no—
142D4—2441no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—1222no—
146C2×C4#1175819812yes—
147C2×C4C2×D24411yescharacteristic
148C2×C4#1175822212yes—
149C2×C4C2×C22⋊D6112yes—
150C2×C4C2×C22⋊D6111yescharacteristic
151C8—24no—
152C8—2442no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—4884no—
157C22—2444no—
158C22—2442no—
159C22C2×#1175819811yescharacteristic
160C22C4×C22⋊D6112yes—
161C4—22no—
162C4—2442no—
163C4#1451974611yescharacteristic
164C4#1451975112yes—
165C4#1451976011yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—4882no—
170C2#1683964111yescharacteristic
subgroupG/H
centerC2#16839641
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#568C2
socleC2×C61#386
hypercenter#568D61
hypocenterC61#1914
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #16839746C2semidirect
3. C2×#14519693C2semidirect
4. #16839534C2semidirect
5. C61×#568C2semidirect
35. M16×C61D4semidirect
86. #568D61semidirect
91. C61#1914semidirect
123. M16C22⋊D61semidirect