Finite Group Databasebeta

← #21444860

Subgroups — #21444860

Order 7808.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840393C211yesmaximal, characteristic
2#16840097C212yesmaximal
3#16839498C212yesmaximal
4#16839488C211yesmaximal, characteristic
5C61×#400C211yesmaximal, characteristic
6#14519776—22no—
7#14519768—22no—
8#14519756—21no—
9#14519756C2212yes—
10#14519736—21no—
11#14519710—22no—
12#14519700—22no—
13C22⋊#92418C2212yes—
14C2×C4⋊C4×C61C2211yescharacteristic
15C2×C4⋊C4×C61C2211yescharacteristic
16#95×C61—21no—
17#95×C61—21no—
18#95×C61C2211yescharacteristic
19C22×C4×C61—21no—
20C22×C4×C61—21no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×Dic122—21no—
25C2×Dic122D412yes—
26C4⋊C4×C61—22no—
27C4⋊C4×C61—22no—
28C22⋊Dic61—22no—
29C4⋊Dic61—21no—
30C4⋊Dic61—21no—
31C4⋊Dic61—21no—
32C4⋊Dic61D412yes—
33#11758196—22no—
34#11758196—22no—
35C4×Dic61—22no—
36C2×#92418—22no—
37C23×C61C2×D411yescharacteristic
38C2×C4×C61—21no—
39C2×C4×C61—21no—
40C2×C4×C61—21no—
41C2×C4×C61—41no—
42C2×C4×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61—42no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61Q1612yes—
49C2×C4×C61C2×D412yes—
50C2×Dic61—22no—
51C2×Dic61—22no—
52Dic122—42no—
53Dic122—81no—
54#92418—42no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61#12011yescharacteristic
58C22×C61C2×Q1611yescharacteristic
59C22×C61#13711yescharacteristic
60C4×C61—22no—
61C4×C61—22no—
62C4×C61—41no—
63C4×C61—81no—
64C4×C61—81no—
65Dic61—42no—
66Dic61—42no—
67#1617—611nomaximal, Sylow
68C2×C61—21no—
69C2×C61—21no—
70C2×C61#45111yescharacteristic
71C2×C61#45411yescharacteristic
72C2×C61#45811yescharacteristic
73#544—611no—
74#484—612no—
75#400D6111yescharacteristic
76#328—612no—
77#324—611no—
78C61#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—1222no—
80#125—1222no—
81C22⋊Q8—612no—
82C22⋊Q8—1221no—
83#117—1221no—
84C2×C4⋊C4C2×D6111yescharacteristic
85C2×C4⋊C4C2×D6111yescharacteristic
86#107—1222no—
87#103—1222no—
88C22⋊C8—612no—
89#95—21no—
90#95—21no—
91#95C2×D6111yescharacteristic
92C2×Q8—612no—
93C2×Q8—1221no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D6111yescharacteristic
97C22×C4C22⋊D6111yescharacteristic
98C22×C4C22×D6111yescharacteristic
99C2×C8—1222no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—612no—
103C4⋊C4—1222no—
104C4⋊C4—1221no—
105C4⋊C4—1221no—
106C4⋊C4—1221no—
107C4⋊C4—1222no—
108C22⋊C4—1222no—
109C42—1222no—
110C23C2×C22⋊D6111yescharacteristic
111Q8—4881no—
112Q8—2442no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—1222no—
124C2×C4—1222no—
125C2×C4#1175820212yes—
126C2×C4D4×D6112yes—
127C8—2442no—
128C22—21no—
129C22—21no—
130C22#1451974511yescharacteristic
131C22C2×#1175820211yescharacteristic
132C22#1451980711yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—2442no—
139C4—2442no—
140C2—21no—
141C2—21no—
142C2#1683991711yescharacteristic
143C2#1683993411yescharacteristic
144C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#400C2
socleC22×C61#120
hypercenter#400D61
hypocenterC61#1617
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
78. C61#1617semidirect