Finite Group Databasebeta

← #21458711

Subgroups — #21458711

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#16840490C212yesmaximal
2#16840167C211yesmaximal, characteristic
3#16840164C212yesmaximal
4#16840070C214yesmaximal
5#16840048C212yesmaximal
6C4×Dic244C212yesmaximal
7C4×Dic244C211yesmaximal, characteristic
8C8×Q8×C61C211yesmaximal, characteristic
9C2×Dic244C2211yescharacteristic
10#14519777C2212yes—
11#14519775—22no—
12#14519769C2214yes—
13#14519767—24no—
14C4×Dic122C2212yes—
15C4×Dic122C2214yes—
16#14519742—22no—
17#14519711C2212yes—
18#14519711C2211yescharacteristic
19#14519711C2212yes—
20#14519709C2214yes—
21#14519702C2214yes—
22#14519702C2212yes—
23C4×Q8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C4⋊C8×C61C2212yes—
26C4×C8×C61C2212yes—
27C4×C8×C61C2211yescharacteristic
28C2×Q8×C61D411yescharacteristic
29C2×Dic122—22no—
30C2×Dic122C2312yes—
31C2×C8×C61C2312yes—
32C2×C8×C61C2311yescharacteristic
33C2×C8×C61C2311yescharacteristic
34C4⋊C4×C61D411yescharacteristic
35C4⋊C4×C61D412yes—
36C42×C61C2312yes—
37C42×C61C2311yescharacteristic
38C4⋊Dic61—22no—
39C4⋊Dic61C2312yes—
40C4⋊Dic61C2314yes—
41#11758196—24no—
42#11758196—22no—
43#11758196—24no—
44#11758196—24no—
45C4×Dic61—24no—
46C4×Dic61—22no—
47Dic244Q814yescomplemented
48Q8×C61—22no—
49C2×C4×C61C2×D412yes—
50C2×C4×C61C2×D412yes—
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—22no—
56C2×Dic61—24no—
57Dic122—22no—
58Dic122—44no—
59Dic122C2×Q814yes—
60C8×C61—22no—
61C8×C61—21no—
62C8×C61C2×Q812yes—
63C22×C61C22×D411yescharacteristic
64C4×C61—22no—
65C4×C61—22no—
66C4×C61—21no—
67C4×C61#13512yes—
68C4×C61C22×Q811yescharacteristic
69C4×C612−1+411yescharacteristic
70Dic61—24no—
71Dic61—44no—
72Dic61—42no—
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×Q8D6111yescharacteristic
83C4×Q16—612no—
84C4×Q16—611no—
85C61#338311yescharacteristic, complemented, Sylow
86C2×Q16—611no—
87C4⋊Q8—612no—
88C4⋊Q8—1222no—
89#125—614no—
90#125—1224no—
91C4×Q8—612no—
92C4×Q8—614no—
93C4×Q8—1222no—
94C4×Q8C2×D6111yescharacteristic
95#107—611no—
96#107—612no—
97#107—612no—
98#106—614no—
99C4⋊C8C2×D6111yescharacteristic
100C4⋊C8C2×D6112yes—
101#103—614no—
102#103—612no—
103C4×C8C2×D6112yes—
104C4×C8C2×D6111yescharacteristic
105C2×Q8—612no—
106C2×Q8—1222no—
107C2×Q8D24411yescharacteristic
108Q16—614no—
109C2×C8C22×D6112yes—
110C2×C8C22×D6111yescharacteristic
111C2×C8C22×D6111yescharacteristic
112C4⋊C4—612no—
113C4⋊C4—614no—
114C4⋊C4—1222no—
115C4⋊C4—1224no—
116C4⋊C4—1224no—
117C4⋊C4—1224no—
118C4⋊C4—1222no—
119C4⋊C4D24411yescharacteristic
120C4⋊C4D24412yes—
121C42—1224no—
122C42—1222no—
123C42C22×D6112yes—
124C42C22×D6111yescharacteristic
125Q8—22no—
126Q8—614no—
127Q8—1222no—
128Q8—2444no—
129C2×C4—1222no—
130C2×C4—1222no—
131C2×C4—1224no—
132C2×C4C2×D24412yes—
133C2×C4C2×D24411yescharacteristic
134C2×C4C2×D24412yes—
135C2×C4C2×D24411yescharacteristic
136C2×C4C23×D6111yescharacteristic
137C8—22no—
138C8—21no—
139C8Q8×D6112yes—
140C22C22×D24411yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—1224no—
145C4—2444no—
146C4—2442no—
147C4#1451979912yes—
148C4C2×Q8×D6111yescharacteristic
149C4#1451982411yescharacteristic
150C2Q8×D24411yescharacteristic
151C2C2×#1451979911yescharacteristic
152C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC8×Q8×C61C2
socleC22×C61C22×D4
hypercenterC8×Q8D61
hypocenterC61#3383
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
47. Dic244Q8semidirect
85. C61#3383semidirect