Finite Group Databasebeta

← #21461326

Subgroups — #21461326

Order 7808.

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

normal subgroups only

This group has 344 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, complemented
2#16840765C211yesmaximal, characteristic, complemented
3#16840620C214yesmaximal, complemented
4C2×#14519773C211yesmaximal, characteristic
5C2×#11758217—21no—
6#14519844C2212yescomplemented
7#14519844C2212yescomplemented
8C4⋊#92420—21no—
9C22⋊#92420—21no—
10C4×#92420—21no—
11C22×D244C411yescharacteristic
12C22×C22⋊D61—21no—
13C22×C22⋊D61—21no—
14#14519773—21no—
15#14519773—21no—
16#14519773C412yes—
17#14519773C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19C22×D4×C61C411yescharacteristic
20C24×C61—21no—
21C23×D61—21no—
22C2×D4×C61—21no—
23C2×D4×C61—42no—
24C2×D4×C61C2×C412yes—
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—22no—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—44no—
31C2×C22⋊D61—42no—
32C2×C22⋊D61—42no—
33C22×Dic61D411yescharacteristic
34C22×Dic61D411yescharacteristic
35C2×D244—21no—
36C2×D244—42no—
37C2×D244C2×C412yes—
38#11758217—42no—
39C2×#92420—22no—
40C2×#92420—22no—
41C4×Dic61C2×C411yescharacteristic
42C4×Dic61D411yescharacteristic
43C4×Dic61D411yescharacteristic
44C4×Dic61C2311yescharacteristic
45C23×C61—22no—
46C23×C61—42no—
47C23×C61—42no—
48C23×C61—42no—
49C23×C61C22⋊C411yescharacteristic
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—42no—
53C22×D61—42no—
54D4×C61—42no—
55D4×C61—42no—
56C2×C4×C61—22no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—44no—
60C22⋊D61—44no—
61C22⋊D61—42no—
62C22⋊D61—42no—
63C22⋊D61—44no—
64C2×Dic61—22no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61D812yes—
68C2×Dic61SD1612yes—
69C2×Dic61C2×D411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71D244—42no—
72D244—42no—
73#92420—42no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—84no—
81C22×C61#10212yes—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—42no—
86C2×D61—84no—
87C4×C61—21no—
88C4×C61#10012yes—
89Dic61—21no—
90Dic61#10212yes—
91Dic61C2×D811yescharacteristic
92Dic61C2×SD1611yescharacteristic
93Dic61AGL(1,ℤ/8)12yes—
94#1545—611nomaximal, Sylow
95C2×C61—22no—
96C2×C61—82no—
97C2×C61C2×#10011yescharacteristic
98C2×C61C2×#10211yescharacteristic
99C2×C61#41811yescharacteristic
100D61—82no—
101C2×#127—611no—
102#431—611no—
103#423—611no—
104#331—614no—
105C61#154511yescharacteristic, complemented, Sylow
106C22×D4—611no—
107C22×D4—1221no—
108C22×D4—1221no—
109C22×D4#692311yescharacteristic
110C2×M16—1221no—
111#127—612no—
112#127—612no—
113#127—1221no—
114#127—1221no—
115C2×C42—611no—
116C4⋊C8—612no—
117C4⋊C8—612no—
118C4⋊C8—1221no—
119C22⋊C8—1221no—
120C4×C8—1221no—
121C24—21no—
122C24—1221no—
123C2×D4—21no—
124C2×D4—42no—
125C2×D4—612no—
126C2×D4—1222no—
127C2×D4—1222no—
128C2×D4—1222no—
129C2×D4—1222no—
130C2×D4—1221no—
131C2×D4—2442no—
132C2×D4—2442no—
133C2×D4—2442no—
134C2×D4—2444no—
135C2×D4C2×#692312yes—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4C2×#692311yescharacteristic
139M16—2442no—
140C2×C8—1222no—
141C2×C8—1222no—
142C42—611no—
143C42—611no—
144C42—611no—
145C42—611no—
146C23—22no—
147C23—42no—
148C23—42no—
149C23—42no—
150C23—1222no—
151C23—2442no—
152C23—2442no—
153C23—2442no—
154C23C22⋊#692311yescharacteristic
155D4—42no—
156D4—42no—
157D4—2442no—
158D4—2444no—
159D4—2442no—
160D4—2442no—
161D4—2444no—
162D4—2444no—
163D4—2442no—
164C2×C4—22no—
165C2×C4—612no—
166C2×C4—612no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—1222no—
172C2×C4C22⋊#692311yescharacteristic
173C2×C4C22×#692311yescharacteristic
174C8—2442no—
175C8—2442no—
176C22—21no—
177C22—21no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—84no—
182C22—4884no—
183C22—2442no—
184C22—2442no—
185C22—2442no—
186C22#1451983912yes—
187C22C2×C22⋊#692311yescharacteristic
188C4—21no—
189C4—612no—
190C4—611no—
191C4—611no—
192C4—612no—
193C4—1221no—
194C4#1451983712yes—
195C2—22no—
196C2—82no—
197C2—4882no—
198C2C2×#1451983711yescharacteristic
199C2C2×#1451983911yescharacteristic
200C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×D4#6923
hypocenterC61#1545
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840779C2semidirect
2. #16840765C2semidirect
3. #16840620C2semidirect
6. #14519844C22semidirect
7. #14519844C22semidirect
105. C61#1545semidirect