Finite Group Databasebeta

← #21460915

Subgroups — #21460915

Order 7808.

172 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D61⋊#101C211yesmaximal, characteristic
2(C2×#6923)⋊Q8C211yesmaximal, characteristic
3#101×D61C211yesmaximal, characteristic
4D61⋊M16—21no—
5C2×C4⋊#6923C411yescharacteristic
6C2×C4×#6923C411yescharacteristic
7#14519838—21no—
8#14519838C412yescomplemented
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11C2×Q8×D61C2211yescharacteristic
12M16×D61—21no—
13#14519696C411yescharacteristic, complemented
14#14519695—21no—
15#101×C61C411yescharacteristic, complemented
16C22×#6923—21no—
17C22×#6923—21no—
18C2×Q8×C61C2×C411yescharacteristic
19Q8×D61—41no—
20Q8×D61—41no—
21C2×C4×D61C2×C411yescharacteristic
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×Dic122C2×C411yescharacteristic
25C2×Dic122D411yescharacteristic
26C2×Dic122Q811yescharacteristic
27#11758217—22no—
28C4⋊#6923—41no—
29C4×#6923—41no—
30#11758213—41no—
31D61⋊C8—41no—
32M16×C61—21no—
33#11758194—21no—
34#11758189—41no—
35C8×D61—41no—
36C22×D61C22⋊C411yescharacteristic
37C2×#6923—22no—
38C2×#6923—41no—
39C2×#6923—41no—
40C2×#6923—42no—
41C2×#6923—41no—
42Q8×C61—41no—
43C2×C4×C61C4211yescharacteristic
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C4⋊C411yescharacteristic
46C2×Dic61C22⋊C411yescharacteristic
47C2×Dic61C4⋊C411yescharacteristic
48C2×Dic61C4⋊C411yescharacteristic
49C4×D61—21no—
50C4×D61—21no—
51C4×D61—21no—
52C4×D61—21no—
53C4×D61—21no—
54C4×D61—21no—
55Dic122—41no—
56Dic122—41no—
57Dic122—41no—
58#92420—42no—
59C8×C61—41no—
60#92418—41no—
61C22×C61#9511yescharacteristic
62C2×D61—21no—
63C2×D61—21no—
64C2×D61#9911yescharacteristic
65C2×D61#9911yescharacteristic
66#6923—42no—
67#6923—81no—
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—21no—
71Dic61—21no—
72Dic61—21no—
73Dic61—21no—
74#1394—611nomaximal, Sylow
75C2×C61—21no—
76C2×C61#34211yescharacteristic
77D61—21no—
78D61#35511yescharacteristic
79D61#35611yescharacteristic
80C2×#101—611no—
81C2×#101—611no—
82#391—611no—
83C61#139411yescharacteristic, complemented, Sylow
84C22×Q8—611no—
85C2×M16—1221no—
86C2×M16—1221no—
87C2×C4⋊C4—611no—
88C2×C42—611no—
89#101—612no—
90#101—611no—
91#101—1221no—
92#101—1221no—
93#101#692311yescharacteristic, complemented
94#95—1221no—
95#95—1221no—
96C2×Q8—611no—
97C2×Q8—611no—
98C2×Q8—611no—
99C2×Q8—2441no—
100C2×Q8—2441no—
101C2×Q8C2×#692311yescharacteristic
102C22×C4—611no—
103C22×C4—611no—
104C22×C4—611no—
105C22×C4—1221no—
106C22×C4—1221no—
107M16—21no—
108M16—1222no—
109M16—1221no—
110M16—2441no—
111M16—2441no—
112C2×C8—2441no—
113C2×C8—2441no—
114C4⋊C4—2441no—
115C42—2441no—
116C23—611no—
117Q8—41no—
118Q8—2441no—
119Q8—2441no—
120Q8—2441no—
121C2×C4—611no—
122C2×C4—611no—
123C2×C4—611no—
124C2×C4—1221no—
125C2×C4—1221no—
126C2×C4—1221no—
127C2×C4—1221no—
128C2×C4—1221no—
129C2×C4—1221no—
130C2×C4—1222no—
131C2×C4—2441no—
132C2×C4—2442no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4C4×#692311yescharacteristic
136C2×C4C4⋊#692311yescharacteristic
137C2×C4C22⋊#692311yescharacteristic
138C8—41no—
139C8—2441no—
140C8—2442no—
141C22—611no—
142C22—611no—
143C22—1221no—
144C22—1221no—
145C22(C2×#6923)⋊C411yescharacteristic
146C4—21no—
147C4—21no—
148C4—21no—
149C4—1221no—
150C4—1221no—
151C4—1221no—
152C4—4881no—
153C4—2442no—
154C2—21no—
155C2—611no—
156C2—611no—
157C2—1221no—
158C2#1684063911yescharacteristic
subgroupG/H
centerC2#16840639
commutatorC2×C4×C61C42
FrattiniC2×Q8C2×#6923
Fitting#101×C61C4
socleC2×C61#342
hypercenter#101#6923
hypocenterC61#1394
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
8. #14519838C4semidirect
13. #14519696C4semidirect
15. #101×C61C4semidirect
83. C61#1394semidirect
93. #101#6923semidirect