Finite Group Databasebeta

← #21458250

Subgroups — #21458250

Order 7808.

340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840482C212yesmaximal
2#16840167C211yesmaximal, characteristic, complemented
3#16840104C214yesmaximal, complemented
4#16840048C212yesmaximal, complemented
5#16840003C212yesmaximal, complemented
6C4×Dic244C211yesmaximal, characteristic, complemented
7#16839800C212yesmaximal, complemented
8C8×D4×C61C211yesmaximal, characteristic
9C2×Dic244C2211yescharacteristic
10#14519777C2212yes—
11#14519770—24no—
12#14519764—22no—
13#14519756C2214yes—
14C4×Dic122C2212yes—
15#14519742—22no—
16#14519736C2214yes—
17#14519711C2212yes—
18#14519711C2211yescharacteristic
19#14519711C2212yes—
20#14519709C2214yes—
21#14519702C2214yes—
22#14519702C2212yes—
23C22×C8×C61C2212yes—
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2212yes—
27C4×C8×C61C2211yescharacteristic
28C2×D4×C61D411yescharacteristic
29C22×C4×C61C2312yes—
30C2×Dic122—22no—
31C2×Dic122C2312yes—
32C2×C8×C61—24no—
33C2×C8×C61C2311yescharacteristic
34C2×C8×C61C2312yes—
35C2×C8×C61C2311yescharacteristic
36C4⋊C4×C61D411yescharacteristic
37C22⋊C4×C61D412yes—
38C42×C61C2311yescharacteristic
39C22⋊Dic61—24no—
40C22⋊Dic61—24no—
41C4⋊Dic61—22no—
42C4⋊Dic61C2312yes—
43C4⋊Dic61C2314yes—
44#11758196—24no—
45#11758196—22no—
46C4×Dic61—24no—
47C4×Dic61—22no—
48Dic244—22no—
49C23×C61C2×D412yes—
50D4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61C2×D412yes—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2411yescharacteristic
57C2×Dic61—22no—
58C2×Dic61—22no—
59C2×Dic61—24no—
60Dic122—22no—
61Dic122—22no—
62Dic122—44no—
63C8×C61—22no—
64C8×C61—21no—
65C8×C61#4112yes—
66C22×C61—22no—
67C22×C61—22no—
68C22×C61—22no—
69C22×C61C22×D411yescharacteristic
70C4×C61—22no—
71C4×C61—21no—
72C4×C61#13512yes—
73C4×C61C2×#4111yescharacteristic
74C4×C612−1+411yescharacteristic
75Dic61—42no—
76Dic61—44no—
77Dic61—42no—
78#3342—611nomaximal, Sylow
79C2×C61—42no—
80C2×C61#54711yescharacteristic
81C2×C61C2×#13511yescharacteristic
82C2×C61#57811yescharacteristic
83#556—612no—
84#500—611no—
85#485—614no—
86#475—612no—
87#467—612no—
88C4×Q16—611no—
89C8×D4D6111yescharacteristic
90#427—612no—
91C61#334211yescharacteristic, complemented, Sylow
92C2×Q16—611no—
93C22×C8C2×D6112yes—
94C4⋊Q8—612no—
95#126—1224no—
96#124—1222no—
97C22⋊Q8—614no—
98C4×Q8—612no—
99C4×Q8—1222no—
100C4×D4C2×D6111yescharacteristic
101#117—614no—
102#107—611no—
103#107—612no—
104#107—612no—
105#106—614no—
106C4⋊C8C2×D6111yescharacteristic
107#103—612no—
108#103—614no—
109C22⋊C8C2×D6112yes—
110C4×C8C2×D6111yescharacteristic
111C2×Q8—612no—
112C2×Q8—1222no—
113C2×D4D24411yescharacteristic
114C22×C4C22×D6112yes—
115Q16—1222no—
116C2×C8—24no—
117C2×C8C22×D6111yescharacteristic
118C2×C8C22×D6112yes—
119C2×C8C22×D6111yescharacteristic
120C4⋊C4—612no—
121C4⋊C4—614no—
122C4⋊C4—1222no—
123C4⋊C4—1224no—
124C4⋊C4—1222no—
125C4⋊C4D24411yescharacteristic
126C22⋊C4—1224no—
127C22⋊C4—1224no—
128C22⋊C4D24412yes—
129C42—1224no—
130C42—1222no—
131C42C22×D6111yescharacteristic
132C23C2×D24412yes—
133Q8—1222no—
134Q8—1222no—
135Q8—2444no—
136D4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—1222no—
140C2×C4—1224no—
141C2×C4—1222no—
142C2×C4C2×D24412yes—
143C2×C4C2×D24411yescharacteristic
144C2×C4C2×D24411yescharacteristic
145C2×C4C23×D6111yescharacteristic
146C8—22no—
147C8—21no—
148C8#1175822412yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22C22×D24411yescharacteristic
153C4—21no—
154C4—22no—
155C4—2444no—
156C4—2442no—
157C4—2442no—
158C4#1451979912yes—
159C4C2×#1175822411yescharacteristic
160C4#1451982411yescharacteristic
161C2—42no—
162C2#1684041611yescharacteristic
163C2C2×#1451979911yescharacteristic
164C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC8×D4×C61C2
socleC22×C61C22×D4
hypercenterC8×D4D61
hypocenterC61#3342
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #16840167C2semidirect
3. #16840104C2semidirect
4. #16840048C2semidirect
5. #16840003C2semidirect
6. C4×Dic244C2semidirect
7. #16839800C2semidirect
91. C61#3342semidirect