Finite Group Databasebeta

← #21461513

Subgroups — #21461513

Order 7808.

372 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×#11758213C211yesmaximal, characteristic
2C2×D61⋊M16C211yesmaximal, characteristic
3#16840638C214yesmaximal, complemented
4C2×M16×D61C211yesmaximal, characteristic
5C2×#11758213—21no—
6C2×#11758213—22no—
7C2×#11758213C414yes—
8C2×#11758213C2212yes—
9C2×#11758213C2212yes—
10D61⋊M16—22no—
11D61⋊M16C414yes—
12C2×#11758217—21no—
13C2×D61⋊C8—21no—
14C22×#92420—21no—
15C22×C4×D61C2211yescharacteristic
16C2×#11758194C411yescharacteristic
17C2×#11758189C412yes—
18M16×D61—22no—
19M16×D61—22no—
20C2×C8×D61C2212yes—
21C2×M16×C61C411yescharacteristic
22C23×D61Q811yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61C2×C412yes—
27C2×C4×D61C2×C412yes—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D412yes—
30C2×C4×D61D412yes—
31C2×C4×D61Q811yescharacteristic
32C2×C4×D61C2311yescharacteristic
33#11758217—24no—
34C2×#92420—24no—
35C2×#92420—22no—
36C2×#92420—22no—
37#11758213—24no—
38#11758213—22no—
39#11758213—22no—
40#11758213C2×C414yes—
41#11758213C2×C414yes—
42D61⋊C8—24no—
43M16×C61—22no—
44C2×C8×C61C2×C412yes—
45#11758194—22no—
46C2×#92418C2×C412yes—
47#11758189—24no—
48C8×D61—22no—
49C8×D61—22no—
50C23×C61C4⋊C411yescharacteristic
51C22×D61—42no—
52C22×D61C4⋊C411yescharacteristic
53C22×D61C4⋊C412yes—
54C22×D61C4⋊C412yes—
55C22×D61C2×Q811yescharacteristic
56C2×C4×C61C4212yes—
57C2×C4×C61C22⋊C412yes—
58C2×C4×C61C4⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61C22⋊C412yes—
61C2×Dic61C22⋊C412yes—
62C2×Dic61C4⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61C4212yes—
65C4×D61C22⋊C412yes—
66C4×D61C22⋊C412yes—
67C4×D61C22⋊C412yes—
68C4×D61C4⋊C412yes—
69C4×D61C4⋊C412yes—
70C4×D61C22×C411yescharacteristic
71C4×D61C22×C411yescharacteristic
72C4×D61C2×D411yescharacteristic
73C4×D61C2×D411yescharacteristic
74#92420—24no—
75#92420—24no—
76C8×C61—22no—
77#92418—22no—
78C22×C61—22no—
79C22×C61#9512yes—
80C22×C61C2×C4⋊C411yescharacteristic
81C2×D61—22no—
82C2×D61—22no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61#9512yes—
86C2×D61C2×C4⋊C411yescharacteristic
87C2×D61C2×C4⋊C411yescharacteristic
88C4×C61#9512yes—
89C4×C61C2×C4211yescharacteristic
90C4×C61C2×C22⋊C411yescharacteristic
91Dic61#9512yes—
92Dic61C2×C22⋊C411yescharacteristic
93Dic61C2×C22⋊C411yescharacteristic
94#1738—611nomaximal, Sylow
95C2×C61—22no—
96C2×C61C2×#9511yescharacteristic
97C2×C61#43012yes—
98D61—22no—
99D61—21no—
100D61—21no—
101C22×M16—611no—
102C22×M16—611no—
103C22×M16—611no—
104#341—614no—
105C61#173811yescharacteristic, complemented, Sylow
106C23×C4—611no—
107C2×M16—611no—
108C2×M16—612no—
109C2×M16—614no—
110C2×M16—614no—
111C2×M16—612no—
112C2×M16—612no—
113C2×M16—1222no—
114C2×M16—1222no—
115C2×M16—1221no—
116C2×M16—1222no—
117C2×M16—1221no—
118C2×M16—1222no—
119C2×M16#692311yescharacteristic
120C22×C8—612no—
121C22×C8—1221no—
122C22×C8—1221no—
123C24—611no—
124C22×C4—611no—
125C22×C4—612no—
126C22×C4—612no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—612no—
130C22×C4—612no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4C2×#692311yescharacteristic
134M16—22no—
135M16—614no—
136M16—614no—
137M16—1224no—
138M16—1224no—
139M16—1222no—
140M16—1222no—
141M16—1224no—
142M16—1222no—
143C2×C8—612no—
144C2×C8—1222no—
145C2×C8—1222no—
146C2×C8—1224no—
147C2×C8—1224no—
148C2×C8—1222no—
149C2×C8—1222no—
150C2×C8C2×#692312yes—
151C23—611no—
152C23—611no—
153C23—612no—
154C23—612no—
155C23—2442no—
156C23C4⋊#692311yescharacteristic
157C2×C4—612no—
158C2×C4—612no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—612no—
162C2×C4—612no—
163C2×C4—612no—
164C2×C4—612no—
165C2×C4—612no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—612no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4C4×#692312yes—
172C2×C4C4⋊#692311yescharacteristic
173C2×C4C22⋊#692312yes—
174C2×C4C22×#692311yescharacteristic
175C8—22no—
176C8—1224no—
177C8—1224no—
178C8—1222no—
179C22—22no—
180C22—612no—
181C22—611no—
182C22—611no—
183C22—1222no—
184C22—1222no—
185C22—2442no—
186C22—2442no—
187C22(C2×#6923)⋊C412yes—
188C22C2×C4⋊#692311yescharacteristic
189C4—612no—
190C4—611no—
191C4—611no—
192C4(C2×#6923)⋊C412yes—
193C4C2×C4×#692311yescharacteristic
194C4C2×C22⋊#692311yescharacteristic
195C2—22no—
196C2—1222no—
197C2—1221no—
198C2—1221no—
199C2C2×(C2×#6923)⋊C411yescharacteristic
200C2#1684077712yes—
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC2×M16×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC2×M16#6923
hypocenterC61#1738
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #16840638C2semidirect
105. C61#1738semidirect