Finite Group Databasebeta

← #21461348

Subgroups — #21461348

Order 7808.

228 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840782C211yesmaximal, characteristic
2#16840782C211yesmaximal, characteristic
3#16840621C214yesmaximal, complemented
4C2×#14519776C211yesmaximal, characteristic
5#14519844C2212yes—
6#14519844C2212yes—
7C22⋊#92420—21no—
8C22⋊#92420—21no—
9#14519832—21no—
10#14519832—21no—
11C22×Dic122—21no—
12#14519776—21no—
13#14519776—21no—
14#14519776C412yes—
15#14519776C2212yes—
16C2×C4⋊Dic61C411yescharacteristic
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×Dic61—21no—
23C22×Dic61D411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×Dic122—22no—
26C2×Dic122—22no—
27C2×Dic122—44no—
28C2×#92420—22no—
29C2×#92420—22no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61C2×C412yes—
32C4⋊Dic61—21no—
33C4⋊Dic61C2×C412yes—
34#11758196—22no—
35#11758196—22no—
36C4×Dic61C2×C411yescharacteristic
37C4×Dic61D411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61C2311yescharacteristic
40C23×C61C22⋊C411yescharacteristic
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—42no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22×C411yescharacteristic
46C2×Dic61—22no—
47C2×Dic61—22no—
48C2×Dic61—22no—
49C2×Dic61—42no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C2×D411yescharacteristic
53C2×Dic61C2×D411yescharacteristic
54Dic122—44no—
55Dic122—44no—
56#92420—42no—
57#92420—42no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61#10112yes—
61C22×C61C2×C22⋊C411yescharacteristic
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—42no—
65Dic61—21no—
66Dic61—21no—
67Dic61—42no—
68Dic61AGL(1,ℤ/8)12yes—
69Dic61#13712yes—
70#1556—611nomaximal, Sylow
71C2×C61—22no—
72C2×C61C2×#10111yescharacteristic
73C2×C61#41811yescharacteristic
74C2×C61#41911yescharacteristic
75C2×C4⋊Q8—611no—
76#432—611no—
77#432—611no—
78#332—614no—
79C61#155611yescharacteristic, complemented, Sylow
80C22×Q8—1221no—
81C4⋊Q8—612no—
82C4⋊Q8—612no—
83C4⋊Q8—1221no—
84C4⋊Q8—1221no—
85C2×C4⋊C4—611no—
86C2×C4⋊C4—1221no—
87C2×C4⋊C4#692311yescharacteristic
88C2×C42—611no—
89C4⋊C8—612no—
90C4⋊C8—612no—
91C22⋊C8—1221no—
92C22⋊C8—1221no—
93#97—1221no—
94#97—1221no—
95C2×Q8—1222no—
96C2×Q8—1222no—
97C2×Q8—2444no—
98C22×C4—21no—
99C22×C4—611no—
100C22×C4—611no—
101C22×C4—1221no—
102C22×C4C2×#692311yescharacteristic
103C2×C8—1222no—
104C2×C8—1222no—
105C4⋊C4—21no—
106C4⋊C4—612no—
107C4⋊C4—1222no—
108C4⋊C4—1222no—
109C4⋊C4—1221no—
110C4⋊C4C2×#692312yes—
111C42—611no—
112C42—611no—
113C42—611no—
114C42—611no—
115C23C22⋊#692311yescharacteristic
116Q8—2444no—
117Q8—2444no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—611no—
122C2×C4—611no—
123C2×C4—611no—
124C2×C4—611no—
125C2×C4—1222no—
126C2×C4—1222no—
127C2×C4—1222no—
128C2×C4—2442no—
129C2×C4C22⋊#692311yescharacteristic
130C2×C4C22×#692311yescharacteristic
131C8—2442no—
132C8—2442no—
133C22—21no—
134C22—21no—
135C22#1451983812yes—
136C22C2×C22⋊#692311yescharacteristic
137C4—21no—
138C4—21no—
139C4—42no—
140C4—612no—
141C4—612no—
142C4—1221no—
143C4—1221no—
144C4—2442no—
145C2—22no—
146C2C2×#1451983811yescharacteristic
147C2#1684075411yescharacteristic
148C2#1684075511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1556
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840621C2semidirect
79. C61#1556semidirect