Finite Group Databasebeta

← #21461946

Subgroups — #21461946

Order 7808.

332 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×#14519840C214yesmaximal
2C4×D61⋊C8C211yesmaximal, characteristic
3#16840708C211yesmaximal, characteristic
4C4⋊Q8×D61C211yesmaximal, characteristic
5C2×D61⋊C8C2212yes—
6C2×C4⋊#6923—22no—
7C2×C4⋊#6923C2212yes—
8#14519840—28no—
9C4×#92420—22no—
10C2×Q8×D61C2212yes—
11#14519777C411yescharacteristic, complemented
12#14519776—22no—
13#14519775C412yescomplemented
14C4⋊C4×D61—22no—
15C42×D61C2211yescharacteristic
16C4⋊Q8×C61C411yescharacteristic, complemented
17C22×#6923—22no—
18C2×Q8×C61C2×C412yes—
19Q8×D61—24no—
20Q8×D61—24no—
21C2×C4×D61—22no—
22C2×C4×D61D412yes—
23C2×C4×D61C2311yescharacteristic
24C2×Dic122—22no—
25C2×Dic122C2×C412yes—
26C2×#92420—22no—
27C4⋊#6923—24no—
28C4⋊#6923—44no—
29D61⋊C8—22no—
30D61⋊C8D414yes—
31C4⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33C4⋊Dic61—22no—
34#11758196—24no—
35C4×Dic61C2×C411yescharacteristic
36C4×Dic61D412yes—
37C22×D61C2×D411yescharacteristic
38C2×#6923—42no—
39C2×#6923—44no—
40Q8×C61—24no—
41C2×C4×C61—22no—
42C2×C4×C61C22⋊C412yes—
43C2×C4×C61C22×C411yescharacteristic
44C2×Dic61—22no—
45C2×Dic61C22⋊C412yes—
46C2×Dic61C2×D411yescharacteristic
47C4×D61—42no—
48C4×D61—42no—
49C4×D61SD1614yes—
50C4×D61Q1614yes—
51C4×D61C2×D412yes—
52C4×D61#4112yes—
53Dic122—24no—
54Dic122—44no—
55#92420—24no—
56C22×C61C2×C22⋊C411yescharacteristic
57C2×D61#12411yescharacteristic
58C2×D61#12711yescharacteristic
59C2×D61C2×SD1612yes—
60C2×D61C2×Q1612yes—
61#6923—82no—
62C4×C61—42no—
63C4×C61#10314yescomplemented
64C4×C61C4×D412yes—
65Dic61—42no—
66Dic61#10314yescomplemented
67Dic61#12112yes—
68#1956—611nomaximal, Sylow
69C2×C61#39011yescharacteristic
70C2×C61C2×#10312yes—
71D61#48712yes—
72D61#49211yescharacteristic
73D61#49411yescharacteristic
74C2×C4⋊Q8—611no—
75C2×#103—614no—
76C2×C4×C8—611no—
77#384—611no—
78C61#195611yescharacteristic, complemented, Sylow
79C22×Q8—612no—
80C22×C8—612no—
81C4⋊Q8—612no—
82C4⋊Q8—611no—
83C4⋊Q8—1222no—
84C4⋊Q8#692311yescharacteristic, complemented
85C2×C4⋊C4—612no—
86C2×C4⋊C4—1222no—
87C2×C4⋊C4—1222no—
88C2×C42—611no—
89#103—1228no—
90C4×C8—1222no—
91C2×Q8—612no—
92C2×Q8—1222no—
93C2×Q8—1224no—
94C2×Q8—1224no—
95C2×Q8C2×#692312yes—
96C22×C4—612no—
97C22×C4—611no—
98C22×C4—1222no—
99C22×C4—1222no—
100C2×C8—614no—
101C2×C8—1222no—
102C2×C8—1222no—
103C4⋊C4—22no—
104C4⋊C4—1224no—
105C4⋊C4—1224no—
106C4⋊C4—1222no—
107C4⋊C4—2444no—
108C42—612no—
109C42—611no—
110C42C2×#692311yescharacteristic
111C23—611no—
112Q8—24no—
113Q8—1224no—
114Q8—2444no—
115C2×C4—22no—
116C2×C4—612no—
117C2×C4—611no—
118C2×C4—614no—
119C2×C4—614no—
120C2×C4—612no—
121C2×C4—612no—
122C2×C4—1222no—
123C2×C4—2442no—
124C2×C4—2442no—
125C2×C4—2442no—
126C2×C4—2444no—
127C2×C4C22⋊#692312yes—
128C2×C4C22×#692311yescharacteristic
129C8—1224no—
130C22—611no—
131C22—611no—
132C22—612no—
133C22—612no—
134C22C2×C22⋊#692311yescharacteristic
135C4—42no—
136C4—612no—
137C4—614no—
138C4—4882no—
139C4—2442no—
140C4#1451984014yescomplemented
141C4D4×#692312yes—
142C2—611no—
143C2—612no—
144C2—611no—
145C2#1684071411yescharacteristic
146C2C2×#1451984012yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1956
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #14519777C4semidirect
13. #14519775C4semidirect
16. C4⋊Q8×C61C4semidirect
63. C4×C61#103semidirect
66. Dic61#103semidirect
78. C61#1956semidirect
84. C4⋊Q8#6923semidirect
140. C4#14519840semidirect