Finite Group Databasebeta

← #21461686

Subgroups — #21461686

Order 7808.

272 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 78 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#16840765C212yesmaximal
2C2×#14519838C212yesmaximal
3#16840642C212yesmaximal
4C2×#14519742C211yesmaximal, characteristic
5C2×#11758217C2214yes—
6#14519844—22no—
7C4⋊#92420—22no—
8#14519838—24no—
9C22×Dic122C2211yescharacteristic
10#14519742—22no—
11#14519742—22no—
12C2×#11758196C411yescharacteristic
13C2×#11758196C2211yescharacteristic
14C2×C4×Dic61C411yescharacteristic
15C2×C4×Dic61C411yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17C2×C4⋊C4×C61C411yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61C2×C411yescharacteristic
21C22×Dic61C2×C411yescharacteristic
22C22×Dic61C2×C411yescharacteristic
23C22×Dic61C2×C411yescharacteristic
24C22×Dic61C2311yescharacteristic
25C2×Dic122—22no—
26C2×Dic122—22no—
27C2×Dic122D412yes—
28C2×Dic122Q812yes—
29#11758217—24no—
30#11758217—24no—
31C2×#92420—24no—
32C4⋊C4×C61—22no—
33#11758196—22no—
34#11758196—22no—
35C4×Dic61—21no—
36C4×Dic61—21no—
37C4×Dic61—21no—
38C4×Dic61—21no—
39C4×Dic61D412yes—
40C4×Dic61D412yes—
41C23×C61C22×C411yescharacteristic
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C22⋊C412yes—
48C2×C4×C61C4⋊C412yes—
49C2×Dic61—21no—
50C2×Dic61—21no—
51C2×Dic61—22no—
52C2×Dic61—21no—
53C2×Dic61—41no—
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61C4⋊C412yes—
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D412yes—
59C2×Dic61C2×Q811yescharacteristic
60C2×Dic61#4112yes—
61Dic122—24no—
62Dic122—24no—
63#92420—44no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61C2×C22⋊C411yescharacteristic
67C22×C61C2×C4⋊C411yescharacteristic
68C22×C61#11711yescharacteristic
69C4×C61—22no—
70C4×C61—22no—
71C4×C61—41no—
72Dic61—22no—
73Dic61—21no—
74Dic61—41no—
75Dic61#10112yescomplemented
76Dic61#12112yes—
77Dic61C22⋊Q812yes—
78#1801—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61#38011yescharacteristic
82C2×C61C2×#10111yescharacteristic
83C2×C61#41311yescharacteristic
84C2×C4×Q8—611no—
85#423—612no—
86C2×#101—612no—
87#343—612no—
88C61#180111yescharacteristic, complemented, Sylow
89C22×Q8—611no—
90C2×M16—614no—
91C4×Q8—1222no—
92C4×Q8—1222no—
93C2×C4⋊C4—611no—
94C2×C4⋊C4—611no—
95C2×C4⋊C4#692311yescharacteristic
96C2×C42—611no—
97C2×C42—611no—
98C2×C42—611no—
99C4⋊C8—1222no—
100C4⋊C8—1222no—
101#101—1224no—
102C2×Q8—612no—
103C2×Q8—612no—
104C2×Q8—1222no—
105C2×Q8—1222no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4C2×#692311yescharacteristic
111C22×C4C2×#692311yescharacteristic
112C22×C4C2×#692311yescharacteristic
113M16—1224no—
114M16—1224no—
115C2×C8—1224no—
116C4⋊C4—22no—
117C4⋊C4—1222no—
118C4⋊C4—1222no—
119C42—612no—
120C42—612no—
121C42—1221no—
122C42—1221no—
123C42—1221no—
124C42—1221no—
125C23C22×#692311yescharacteristic
126Q8—1224no—
127Q8—1224no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—611no—
134C2×C4—612no—
135C2×C4—611no—
136C2×C4—611no—
137C2×C4—612no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—1222no—
141C2×C4—1221no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—2441no—
145C2×C4C4⋊#692312yes—
146C2×C4C22⋊#692312yes—
147C8—2444no—
148C22—21no—
149C22—21no—
150C22C2×C22⋊#692311yescharacteristic
151C22C2×C4⋊#692311yescharacteristic
152C22#1451985611yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—612no—
157C4—612no—
158C4—612no—
159C4—1222no—
160C4—1221no—
161C4—2441no—
162C2—21no—
163C2—21no—
164C2#1684070411yescharacteristic
165C2D61⋊#10111yescharacteristic
166C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1801
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
75. Dic61#101semidirect
88. C61#1801semidirect