Finite Group Databasebeta

← #21461722

Subgroups — #21461722

Order 7808.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16840635C214yesmaximal, complemented
4C2×C4⋊C4×D61C211yesmaximal, characteristic
5C2×D61⋊C8C2212yes—
6C2×C4⋊#6923C2212yes—
7C2×C22⋊#6923—21no—
8#14519834—21no—
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11C22×C4×D61—21no—
12C22×C4×D61C2211yescharacteristic
13C2×C4⋊Dic61C411yescharacteristic, complemented
14C2×#11758196—21no—
15C4⋊C4×D61—21no—
16C4⋊C4×D61—21no—
17C4⋊C4×D61C412yescomplemented
18C4⋊C4×D61C2212yes—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C23×D61D411yescharacteristic
21C22×#6923—22no—
22C22×C4×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61—21no—
25C22×Dic61D411yescharacteristic
26C2×C4×D61—24no—
27C2×C4×D61—22no—
28C2×C4×D61—22no—
29C2×C4×D61—42no—
30C2×C4×D61—42no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61C2311yescharacteristic
35C22⋊#6923—42no—
36C2×#92420—22no—
37C4⋊#6923—24no—
38D61⋊C8—24no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61C2×C412yes—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C412yes—
43#11758196—22no—
44#11758196—22no—
45C23×C61C22⋊C411yescharacteristic
46C22×D61—22no—
47C22×D61—22no—
48C22×D61C22⋊C411yescharacteristic
49C22×D61D812yes—
50C22×D61SD1612yes—
51C22×D61C2×D411yescharacteristic
52C2×#6923—42no—
53C2×#6923—42no—
54C2×#6923—42no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61—22no—
61C2×Dic61—22no—
62C2×Dic61—42no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65C4×D61—22no—
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—44no—
69C4×D61—42no—
70C4×D61—42no—
71C4×D61#4114yes—
72#92420—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#10212yes—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—21no—
78C2×D61—21no—
79C2×D61—24no—
80C2×D61—24no—
81C2×D61#10212yes—
82C2×D61#12312yes—
83C2×D61C2×D811yescharacteristic
84C2×D61C2×SD1611yescharacteristic
85C2×D61#13712yes—
86#6923—82no—
87C4×C61—21no—
88C4×C61—42no—
89C4×C61#11712yes—
90Dic61—21no—
91Dic61—42no—
92Dic61#12312yes—
93#1823—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61#38111yescharacteristic
96C2×C61C2×#10211yescharacteristic
97C2×C61#41911yescharacteristic
98D61—22no—
99D61#48012yes—
100D61#48312yes—
101C22×C4⋊C4—611no—
102C2×C22⋊C8—611no—
103#380—611no—
104#340—614no—
105C61#182311yescharacteristic, complemented, Sylow
106C23×C4—611no—
107C23×C4—1221no—
108C22×C8—612no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4—612no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—1221no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4#692311yescharacteristic, complemented
117C2×C22⋊C4—1221no—
118C22⋊C8—1221no—
119C22⋊C8—1221no—
120#95—1221no—
121C24—611no—
122C22×C4—21no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—1224no—
129C22×C4—1222no—
130C22×C4—1222no—
131C22×C4—1221no—
132C22×C4—1222no—
133C22×C4—2442no—
134C22×C4—2442no—
135C22×C4C2×#692311yescharacteristic
136C2×C8—1222no—
137C2×C8—1224no—
138C4⋊C4—21no—
139C4⋊C4—612no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—1224no—
143C4⋊C4—1221no—
144C4⋊C4C2×#692312yes—
145C22⋊C4—2442no—
146C23—611no—
147C23—612no—
148C23—612no—
149C23—611no—
150C23—1222no—
151C23—1222no—
152C23C22⋊#692311yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—611no—
157C2×C4—614no—
158C2×C4—611no—
159C2×C4—1222no—
160C2×C4—1222no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4—2444no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4C22⋊#692311yescharacteristic
172C2×C4C22×#692311yescharacteristic
173C8—2442no—
174C22—21no—
175C22—21no—
176C22—612no—
177C22—611no—
178C22—611no—
179C22—612no—
180C22—612no—
181C22—1224no—
182C22—1224no—
183C22—1221no—
184C22—1221no—
185C22#1451983912yes—
186C22C2×C22⋊#692311yescharacteristic
187C4—21no—
188C4—42no—
189C4—612no—
190C4—1221no—
191C4—4882no—
192C4—2442no—
193C4#1451985612yes—
194C2—22no—
195C2—612no—
196C2—612no—
197C2—1222no—
198C2#1684070511yescharacteristic
199C2C2×#1451983911yescharacteristic
200C2#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#1823
LCSG ▷ C2×C4×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
3. #16840635C2semidirect
13. C2×C4⋊Dic61C4semidirect
17. C4⋊C4×D61C4semidirect
19. C2×C4⋊C4×C61C4semidirect
105. C61#1823semidirect
116. C2×C4⋊C4#6923semidirect