Finite Group Databasebeta

← #21458708

Subgroups — #21458708

Order 7808.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840491C212yesmaximal
2#16840167C211yesmaximal, characteristic
3#16840163C212yesmaximal
4#16840071C214yesmaximal
5#16840047C212yesmaximal
6C8×Dic122C211yesmaximal, characteristic
7Q16×Dic61C212yesmaximal
8C4×Q16×C61C211yesmaximal, characteristic
9#14519777—22no—
10#14519777C2212yes—
11#14519768—24no—
12#14519768C2214yes—
13Q8×Dic61C2214yes—
14C4×Dic122—22no—
15C4×Dic122C2211yescharacteristic
16#14519711C2212yes—
17#14519711C2212yes—
18#14519708C2214yes—
19C4⋊#92418C2211yescharacteristic
20#14519706C2212yes—
21#14519701C2214yes—
22C8×Dic61C2212yes—
23C2×Q16×C61C2211yescharacteristic
24C4×Q8×C61C2212yes—
25#107×C61C2211yescharacteristic
26#103×C61C2212yes—
27C4×C8×C61C2211yescharacteristic
28C2×Q8×C61C2312yes—
29C2×Dic122—22no—
30C2×Dic122D411yescharacteristic
31Q16×C61Q814yescomplemented
32C2×C8×C61C2311yescharacteristic
33C2×C8×C61C2311yescharacteristic
34C4⋊C4×C61—22no—
35C4⋊C4×C61C2312yes—
36C42×C61—22no—
37C42×C61C2311yescharacteristic
38C4⋊Dic61—22no—
39C4⋊Dic61—24no—
40C4⋊Dic61—24no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61C2314yes—
43#11758196—24no—
44#11758196D412yes—
45C4×Dic61—24no—
46C4×Dic61C2312yes—
47C2×#92418C2312yes—
48Q8×C61—22no—
49Q8×C61C2×Q814yes—
50C2×C4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2411yescharacteristic
55C2×Dic61—24no—
56C2×Dic61C2×D412yes—
57C2×Dic61C2×D412yes—
58Dic122—22no—
59Dic122—44no—
60C8×C61—21no—
61C8×C61C2×Q812yes—
62#92418—22no—
63C22×C61C22×D411yescharacteristic
64C4×C61—24no—
65C4×C61—21no—
66C4×C61—42no—
67C4×C61#13512yes—
68C4×C61C22×Q811yescharacteristic
69C4×C612−1+411yescharacteristic
70Dic61—22no—
71Dic61—22no—
72Dic61—44no—
73#3383—611nomaximal, Sylow
74C2×C61D4×Q811yescharacteristic
75C2×C61C2×#13511yescharacteristic
76C2×C61#57811yescharacteristic
77#557—612no—
78#500—611no—
79#499—612no—
80#479—614no—
81#475—612no—
82C8×Q8—611no—
83C4×Q16—612no—
84C4×Q16D6111yescharacteristic
85C61#338311yescharacteristic, complemented, Sylow
86C2×Q16C2×D6111yescharacteristic
87C4⋊Q8—612no—
88C4⋊Q8—1222no—
89#125—614no—
90#125—1224no—
91C4×Q8—611no—
92C4×Q8—614no—
93C4×Q8—1222no—
94C4×Q8C2×D6112yes—
95#107—612no—
96#107—612no—
97#107C2×D6111yescharacteristic
98#106—614no—
99C4⋊C8—612no—
100C4⋊C8—611no—
101#103—614no—
102#103C2×D6112yes—
103C4×C8—612no—
104C4×C8C2×D6111yescharacteristic
105C2×Q8—611no—
106C2×Q8—1222no—
107C2×Q8C22×D6112yes—
108Q16Dic12214yescomplemented
109C2×C8—612no—
110C2×C8C22×D6111yescharacteristic
111C2×C8C22×D6111yescharacteristic
112C4⋊C4—22no—
113C4⋊C4—612no—
114C4⋊C4—611no—
115C4⋊C4—614no—
116C4⋊C4—1224no—
117C4⋊C4—1224no—
118C4⋊C4—1224no—
119C4⋊C4—1222no—
120C4⋊C4C22×D6112yes—
121C42—22no—
122C42—612no—
123C42—1224no—
124C42C22×D6111yescharacteristic
125Q8—22no—
126Q8—1222no—
127Q8—2444no—
128Q8C2×Dic12214yes—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—612no—
132C2×C4—612no—
133C2×C4—1224no—
134C2×C4D4×D6111yescharacteristic
135C2×C4D4×D6111yescharacteristic
136C2×C4C23×D6111yescharacteristic
137C8—21no—
138C8—1222no—
139C8C2×Dic12212yes—
140C22C2×D4×D6111yescharacteristic
141C4—21no—
142C4—24no—
143C4—42no—
144C4—1222no—
145C4—1222no—
146C4—2444no—
147C4#1451980012yes—
148C4C22×Dic12211yescharacteristic
149C4#1451982411yescharacteristic
150C2D4×Dic12211yescharacteristic
151C2C2×#1451980011yescharacteristic
152C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3383
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
31. Q16×C61Q8semidirect
85. C61#3383semidirect
108. Q16Dic122semidirect