Finite Group Databasebeta

← #21456200

Subgroups — #21456200

Order 7808.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840319C211yesmaximal, characteristic
2C2×#14519777C211yesmaximal, characteristic
3#16840131C214yesmaximal, complemented
4#16840113C214yesmaximal, complemented
5#16839772C214yesmaximal
6C4×M16×C61C211yesmaximal, characteristic
7C22×Dic122C2212yes—
8#14519777—22no—
9#14519777C2212yes—
10#14519777C2212yes—
11#14519777C2212yes—
12#14519769C2212yes—
13#14519756—22no—
14C4×Dic122—22no—
15#14519736C2212yes—
16C2×C4⋊Dic61—22no—
17#14519702C22116yes—
18C2×M16×C61C2212yes—
19C2×C42×C61C2211yescharacteristic
20#97×C61C2212yes—
21C4×C8×C61C2212yes—
22C22×C4×C61D412yes—
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—22no—
25C2×Dic122—28no—
26C2×Dic122—22no—
27C2×Dic122—22no—
28C2×Dic122C2314yes—
29M16×C61—24no—
30C2×C8×C61C2314yes—
31C42×C61D412yes—
32C42×C61C2311yescharacteristic
33C42×C61C2311yescharacteristic
34C22⋊Dic61—22no—
35C4⋊Dic61—24no—
36C4⋊Dic61—24no—
37C4⋊Dic61—22no—
38C4⋊Dic61C2314yes—
39#11758196—24no—
40C4×Dic61—22no—
41C23×C61C2×D411yescharacteristic
42C2×C4×C61—24no—
43C2×C4×C61C2×D412yes—
44C2×C4×C61C2×D411yescharacteristic
45C2×C4×C61C2×D412yes—
46C2×C4×C61#4114yes—
47C2×C4×C61C2411yescharacteristic
48C2×Dic61—24no—
49C2×Dic61—24no—
50C2×Dic61—44no—
51Dic122—28no—
52Dic122—44no—
53Dic122—44no—
54C8×C61—24no—
55C22×C61—22no—
56C22×C61#12412yes—
57C22×C61C22×D411yescharacteristic
58C4×C61—22no—
59C4×C61#12412yes—
60C4×C61#13714yes—
61C4×C61C2×#4112yes—
62Dic61—44no—
63Dic61—44no—
64#3139—611nomaximal, Sylow
65C2×C61—22no—
66C2×C61C2×#12411yescharacteristic
67C2×C61C2×#13712yes—
68#533—611no—
69C2×C4⋊Q8—611no—
70#491—614no—
71#487—614no—
72#419—614no—
73C4×M16D6111yescharacteristic
74C61#313911yescharacteristic, complemented, Sylow
75C22×Q8—612no—
76C2×M16C2×D6112yes—
77C4⋊Q8—612no—
78C4⋊Q8—612no—
79C4⋊Q8—612no—
80C4⋊Q8—1222no—
81#125—612no—
82C22⋊Q8—1222no—
83C4×Q8—1222no—
84#117—612no—
85C2×C4⋊C4—1222no—
86C2×C42C2×D6111yescharacteristic
87#103—6116no—
88#97C2×D6112yes—
89C4×C8C2×D6112yes—
90C2×Q8—614no—
91C2×Q8—1222no—
92C2×Q8—1222no—
93C2×Q8—1228no—
94C22×C4—1222no—
95C22×C4D24412yes—
96C22×C4C22×D6111yescharacteristic
97M16—24no—
98C2×C8C22×D6114yes—
99C4⋊C4—614no—
100C4⋊C4—1224no—
101C4⋊C4—1224no—
102C4⋊C4—1224no—
103C4⋊C4—1222no—
104C22⋊C4—1222no—
105C42—1222no—
106C42D24412yes—
107C42C22×D6111yescharacteristic
108C42C22×D6111yescharacteristic
109C23C2×D24411yescharacteristic
110Q8—1228no—
111Q8—2444no—
112Q8—2444no—
113C2×C4—24no—
114C2×C4—1224no—
115C2×C4—1224no—
116C2×C4—2444no—
117C2×C4C2×D24412yes—
118C2×C4C2×D24412yes—
119C2×C4C2×D24411yescharacteristic
120C2×C4#1175822214yes—
121C2×C4C23×D6111yescharacteristic
122C8—24no—
123C22—22no—
124C22#1451976512yes—
125C22C22×D24411yescharacteristic
126C4—22no—
127C4—2444no—
128C4—2444no—
129C4#1451976512yes—
130C4#1451981014yes—
131C4C2×#1175822212yes—
132C2—22no—
133C2C2×#1451976511yescharacteristic
134C2C2×#1451981012yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×M16×C61C2
socleC22×C61C22×D4
hypercenterC4×M16D61
hypocenterC61#3139
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #16840131C2semidirect
4. #16840113C2semidirect
74. C61#3139semidirect