Finite Group Databasebeta

← #21446987

Subgroups — #21446987

Order 7808.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840388C211yesmaximal, characteristic
2#16839623C212yesmaximal
3#16839623C211yesmaximal, characteristic
4#16839528C212yesmaximal
5C61×#342C211yesmaximal, characteristic
6C23×Dic61C2211yescharacteristic
7#14519756—22no—
8#14519754—24no—
9C2×C22⋊Dic61C2211yescharacteristic
10C2×C22⋊Dic61C2212yes—
11#14519684—22no—
12#14519684—24no—
13C2×C22⋊C4×C61C2212yes—
14C2×C22⋊C4×C61C2211yescharacteristic
15C24×C61C2311yescharacteristic
16C22×C4×C61—22no—
17C22×C4×C61D412yes—
18C22×Dic61—21no—
19C22×Dic61—22no—
20C22×Dic61—22no—
21C22×Dic61—21no—
22C22×Dic61—21no—
23C22×Dic61D414yes—
24C22×Dic61Q812yescomplemented
25C2×Dic122—22no—
26C22⋊C4×C61—22no—
27C22⋊C4×C61—22no—
28C22⋊C4×C61—22no—
29C22⋊Dic61—22no—
30C22⋊Dic61—22no—
31C22⋊Dic61—22no—
32C4⋊Dic61—22no—
33#11758196—24no—
34C23×C61—42no—
35C23×C61C2×D411yescharacteristic
36C23×C61C2×D412yes—
37C23×C61C2×Q811yescharacteristic
38C23×C61#4112yes—
39C23×C61#4111yescharacteristic
40C2×C4×C61—22no—
41C2×C4×C61—42no—
42C2×C4×C61—44no—
43C2×C4×C61—42no—
44C2×Dic61—24no—
45C2×Dic61—24no—
46C2×Dic61—22no—
47C2×Dic61—41no—
48C2×Dic61—42no—
49C2×Dic61—41no—
50C2×Dic61—44no—
51C2×Dic61—42no—
52C2×Dic61—41no—
53Dic122—82no—
54C22×C61—22no—
55C22×C61—24no—
56C22×C61—41no—
57C22×C61—42no—
58C22×C61—41no—
59C22×C61#12011yescharacteristic
60C22×C61C22⋊Q812yes—
61C22×C61C22⋊Q811yescharacteristic
62C22×C61#12412yes—
63C22×C61#12411yescharacteristic
64C4×C61—42no—
65C4×C61—82no—
66Dic61—42no—
67Dic61—44no—
68Dic61—81no—
69#2030—611nomaximal, Sylow
70C2×C61—21no—
71C2×C61—22no—
72C2×C61—22no—
73C2×C61—21no—
74C2×C61#39311yescharacteristic
75C2×C61#45812yes—
76#543—611no—
77#381—612no—
78#381—611no—
79#342—612no—
80#342D6111yescharacteristic
81C61#203011yescharacteristic, complemented, Sylow
82C23×C4—611no—
83C22⋊Q8—1224no—
84C22⋊Q8—1222no—
85C2×C22⋊C4—612no—
86C2×C22⋊C4—611no—
87C2×C22⋊C4C2×D6112yes—
88C2×C22⋊C4C2×D6111yescharacteristic
89#95—1224no—
90#95—1222no—
91C24C22×D6111yescharacteristic
92C2×Q8—1222no—
93C22×C4—22no—
94C22×C4—612no—
95C22×C4—614no—
96C22×C4—1221no—
97C22×C4—1222no—
98C22×C4—1222no—
99C22×C4—1221no—
100C22×C4—1221no—
101C22×C4D24412yes—
102C4⋊C4—1224no—
103C4⋊C4—1222no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—1222no—
108C22⋊C4—1222no—
109C22⋊C4—1222no—
110C23—42no—
111C23C2×D24411yescharacteristic
112C23#1175822212yes—
113C23D4×D6112yes—
114C23#1175822411yescharacteristic
115C23Q8×D6111yescharacteristic
116Q8—4882no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—1224no—
122C2×C4—1224no—
123C2×C4—1222no—
124C2×C4—2442no—
125C2×C4—2441no—
126C2×C4—2441no—
127C2×C4—2442no—
128C2×C4—2441no—
129C2×C4—2444no—
130C22—22no—
131C22—24no—
132C22—42no—
133C22—41no—
134C22—41no—
135C22#1451974711yescharacteristic
136C22#1451975512yes—
137C22#1451975711yescharacteristic
138C22#1451976312yes—
139C22#1451976511yescharacteristic
140C4—42no—
141C4—82no—
142C4—4881no—
143C4—2444no—
144C4—2442no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#1683967511yescharacteristic
150C2#1683995312yes—
subgroupG/H
centerC22#14519747
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#342C2
socleC22×C61#120
hypercenter#342D61
hypocenterC61#2030
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
24. C22×Dic61Q8semidirect
81. C61#2030semidirect