Finite Group Databasebeta

← #21462078

Subgroups — #21462078

Order 7808.

266 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 54 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#16840748C211yesmaximal, characteristic, complemented
2#16840741C211yesmaximal, characteristic, complemented
3#16840662C214yesmaximal, complemented
4#16840329C211yesmaximal, characteristic
5D61⋊M16—21no—
6#14519856—21no—
7#14519838—21no—
8#14519837C2212yes—
9#14519836—21no—
10#14519835C2212yes—
11C2×#11758222C2211yescharacteristic
12#14519773—21no—
13#14519764—21no—
14#14519748—21no—
15#14519748—21no—
16#14519746C412yescomplemented
17#14519746C2212yes—
18#14519736C411yescharacteristic, complemented
19C22×D4×C61C411yescharacteristic, complemented
20C24×C61C2×C412yes—
21C2×D4×C61—21no—
22C2×D4×C61—21no—
23C2×D4×C61—41no—
24C2×D4×C61—41no—
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61C2×C411yescharacteristic
29C2×C22⋊D61C2311yescharacteristic
30#11758222—41no—
31#11758222—41no—
32C2×D244D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×Dic122D411yescharacteristic
36C22⋊#6923—22no—
37#11758217—22no—
38C4⋊#6923—41no—
39C4×#6923—41no—
40#11758213—41no—
41D61⋊C8—41no—
42C22⋊Dic61—22no—
43C22⋊Dic61—22no—
44C22⋊Dic61C2×C412yes—
45C4⋊Dic61—21no—
46C4×Dic61—21no—
47C23×C61—22no—
48C23×C61—42no—
49C23×C61—82no—
50C23×C61C22×C411yescharacteristic
51C22×D61C22⋊C411yescharacteristic
52C22×D61C2×D411yescharacteristic
53C2×#6923—42no—
54D4×C61—42no—
55D4×C61—41no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C22⋊D61—41no—
62C22⋊D61—41no—
63C22⋊D61—82no—
64C22⋊D61—82no—
65C2×Dic61—22no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68D244—41no—
69C4×D61—21no—
70C4×D61—21no—
71C4×D61—21no—
72C4×D61—21no—
73Dic122—41no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—41no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—84no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—41no—
85C2×D61—41no—
86#6923—82no—
87C4×C61—21no—
88C4×C61#9911yescharacteristic
89C4×C61#9911yescharacteristic
90Dic61—21no—
91Dic61—21no—
92Dic61—42no—
93#2122—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—41no—
96C2×C61—82no—
97C2×C61C2×#9911yescharacteristic
98D61—41no—
99D61—41no—
100#535—611no—
101#413—611no—
102#410—611no—
103AΣL(1,𝔽16)—614no—
104C61#212211yescharacteristic, complemented, Sylow
105C2×#41—611no—
106C22×D4#692311yescharacteristic, complemented
107C2×M16—1221no—
108#127—1221no—
109#124—1221no—
110#121—1221no—
111#121—1221no—
112#120—612no—
113#120—612no—
114#117—611no—
115#117—1221no—
116#101—1221no—
117#100—612no—
118#99—612no—
119#99—1221no—
120C24C2×#692312yes—
121#41—2441no—
122#41—2441no—
123C2×Q8—611no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4—611no—
129C2×D4—611no—
130C2×D4—611no—
131C2×D4—1222no—
132C2×D4—1222no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4C2×#692311yescharacteristic
136M16—1222no—
137M16—2441no—
138C2×C8—2441no—
139C4⋊C4—1221no—
140C4⋊C4—2441no—
141C22⋊C4—612no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—1221no—
146C42—2441no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23—611no—
151C23—611no—
152C23C22×#692311yescharacteristic
153Q8—2441no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—4882no—
158D4—4882no—
159D4—2441no—
160D4—2441no—
161D4—2441no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1222no—
171C2×C4—2442no—
172C2×C4C22⋊#692311yescharacteristic
173C2×C4C22⋊#692311yescharacteristic
174C8—2442no—
175C22—21no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—84no—
181C22—1221no—
182C22—1221no—
183C22—2441no—
184C22—2441no—
185C22C2×C22⋊#692311yescharacteristic
186C4—21no—
187C4—1221no—
188C4—1221no—
189C4—4882no—
190C4—2442no—
191C4#1451983511yescharacteristic
192C4#1451983511yescharacteristic
193C2—21no—
194C2—41no—
195C2—82no—
196C2—2441no—
197C2—2441no—
198C2C2×#1451983511yescharacteristic
subgroupG/H
centerC2C2×#14519835
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC22×D4×C61C4
socleC2×C61C2×#99
hypercenterC22×D4#6923
hypocenterC61#2122
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840748C2semidirect
2. #16840741C2semidirect
3. #16840662C2semidirect
16. #14519746C4semidirect
18. #14519736C4semidirect
19. C22×D4×C61C4semidirect
104. C61#2122semidirect
106. C22×D4#6923semidirect