Finite Group Databasebeta

← #21461332

Subgroups — #21461332

Order 7808.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#16840779C211yesmaximal, characteristic
2#16840765C211yesmaximal, characteristic
3#16840622C214yesmaximal, complemented
4C2×#14519775C211yesmaximal, characteristic
5C2×#11758217—21no—
6#14519844C2212yes—
7#14519844C2212yes—
8C4⋊#92420—21no—
9C22⋊#92420—21no—
10C4×#92420—21no—
11C22×Dic122C411yescharacteristic
12#14519775—21no—
13#14519775—21no—
14#14519775C412yes—
15#14519775C2212yes—
16C2×#11758196—21no—
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C22×Q8×C61C411yescharacteristic
20C2×Q8×C61—21no—
21C2×Q8×C61—42no—
22C2×Q8×C61C2×C412yes—
23C22×C4×C61—21no—
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×Dic122—21no—
29C2×Dic122—42no—
30C2×Dic122C2×C412yes—
31#11758217—42no—
32C2×#92420—22no—
33C2×#92420—22no—
34#11758196—22no—
35#11758196—22no—
36#11758196—22no—
37#11758196—22no—
38C4×Dic61C2×C411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61C2311yescharacteristic
42C23×C61C22⋊C411yescharacteristic
43Q8×C61—42no—
44Q8×C61—42no—
45C2×C4×C61—22no—
46C2×C4×C61—22no—
47C2×C4×C61—42no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22×C411yescharacteristic
50C2×Dic61—22no—
51C2×Dic61—22no—
52C2×Dic61—42no—
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61SD1612yes—
56C2×Dic61Q1612yes—
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59Dic122—42no—
60Dic122—42no—
61#92420—42no—
62#92420—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61#10312yes—
66C22×C61C2×C22⋊C411yescharacteristic
67C4×C61—21no—
68C4×C61—42no—
69C4×C61#10012yes—
70Dic61—21no—
71Dic61—42no—
72Dic61#10312yes—
73Dic61C2×SD1611yescharacteristic
74Dic61C2×Q1611yescharacteristic
75Dic61#13712yes—
76#1548—611nomaximal, Sylow
77C2×C61—22no—
78C2×C61C2×#10011yescharacteristic
79C2×C61C2×#10311yescharacteristic
80C2×C61#41911yescharacteristic
81C2×C4⋊Q8—611no—
82#431—611no—
83#423—611no—
84#333—614no—
85C61#154811yescharacteristic, complemented, Sylow
86C22×Q8—611no—
87C22×Q8#692311yescharacteristic
88C2×M16—1221no—
89C4⋊Q8—612no—
90C4⋊Q8—612no—
91C4⋊Q8—1221no—
92C4⋊Q8—1221no—
93C2×C4⋊C4—1221no—
94C2×C4⋊C4—1221no—
95C2×C42—611no—
96C4⋊C8—612no—
97C4⋊C8—612no—
98C4⋊C8—1221no—
99C22⋊C8—1221no—
100C4×C8—1221no—
101C2×Q8—21no—
102C2×Q8—42no—
103C2×Q8—612no—
104C2×Q8—1221no—
105C2×Q8—2442no—
106C2×Q8C2×#692312yes—
107C22×C4—21no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4—1221no—
111C22×C4C2×#692311yescharacteristic
112M16—2442no—
113C2×C8—1222no—
114C2×C8—1222no—
115C4⋊C4—1222no—
116C4⋊C4—1222no—
117C4⋊C4—1222no—
118C4⋊C4—1222no—
119C42—611no—
120C42—611no—
121C42—611no—
122C42—611no—
123C23C22⋊#692311yescharacteristic
124Q8—42no—
125Q8—42no—
126Q8—2442no—
127Q8—2442no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—612no—
132C2×C4—612no—
133C2×C4—611no—
134C2×C4—611no—
135C2×C4—611no—
136C2×C4—611no—
137C2×C4—1222no—
138C2×C4—1222no—
139C2×C4—2442no—
140C2×C4C22⋊#692311yescharacteristic
141C2×C4C22×#692311yescharacteristic
142C8—2442no—
143C8—2442no—
144C22—21no—
145C22—21no—
146C22#1451984012yes—
147C22C2×C22⋊#692311yescharacteristic
148C4—21no—
149C4—42no—
150C4—612no—
151C4—611no—
152C4—611no—
153C4—612no—
154C4—1221no—
155C4—2442no—
156C4#1451983712yes—
157C2—22no—
158C2C2×#1451983711yescharacteristic
159C2C2×#1451984011yescharacteristic
160C2#1684075511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×Q8#6923
hypocenterC61#1548
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #16840622C2semidirect
85. C61#1548semidirect