Finite Group Databasebeta

← D61⋊#349 #21462053

Subgroups — D61⋊#349 #21462053

Order 7808.

236 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 74 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⋊M32C212yesmaximal, complemented
2#16840659C212yesmaximal, complemented
3#16840658C212yesmaximal, complemented
4C2×M16×D61C211yesmaximal, characteristic
5#14519852—22no—
6#14519851C2214yescomplemented
7D61⋊C16—22no—
8C22×C4×D61C411yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758189C411yescharacteristic
11C2×#11758189C2211yescharacteristic
12M16×D61—22no—
13M16×D61—22no—
14C2×C8×D61C411yescharacteristic
15C2×C8×D61C2211yescharacteristic
16C2×M16×C61C411yescharacteristic
17C23×D61C811yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61C811yescharacteristic
20C2×C4×D61—21no—
21C2×C4×D61—21no—
22C2×C4×D61—21no—
23C2×C4×D61—21no—
24C2×C4×D61C811yescharacteristic
25C2×C4×D61C811yescharacteristic
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61C2×C411yescharacteristic
28M16×C61—22no—
29C2×C8×C61C2×C411yescharacteristic
30C2×C8×C61C2×C411yescharacteristic
31#11758194—22no—
32C2×#92418C2×C411yescharacteristic
33C2×#92418C2311yescharacteristic
34#11758189—22no—
35#11758189—22no—
36C8×D61—21no—
37C8×D61—21no—
38C8×D61D412yes—
39C8×D61D412yes—
40#11758187—24no—
41C23×C61C2×C811yescharacteristic
42C22×D61—21no—
43C22×D61—21no—
44C22×D61—42no—
45C22×D61C2×C811yescharacteristic
46C22×D61C2×C811yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61C2×C811yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C2×Dic61—21no—
52C2×Dic61—21no—
53C2×Dic61C2×C811yescharacteristic
54C2×Dic61C2×C811yescharacteristic
55C4×D61—21no—
56C4×D61—21no—
57C4×D61—21no—
58C4×D61—21no—
59C4×D61—21no—
60C4×D61—21no—
61C4×D61C22⋊C411yescharacteristic
62C4×D61C22⋊C411yescharacteristic
63C4×D61M1611yescharacteristic
64C4×D61M1611yescharacteristic
65C8×C61—21no—
66C8×C61C22⋊C412yes—
67#92418—21no—
68#92418C2×D412yes—
69C22×C61—21no—
70C22×C61—41no—
71C22×C61C22×C811yescharacteristic
72C2×D61—22no—
73C2×D61—21no—
74C2×D61—42no—
75C2×D61—42no—
76C2×D61—41no—
77C2×D61C22⋊C811yescharacteristic
78C2×D61C22⋊C811yescharacteristic
79C4×C61—21no—
80C4×C61C2×C22⋊C411yescharacteristic
81C4×C61C2×M1611yescharacteristic
82Dic61—21no—
83Dic61C22⋊C811yescharacteristic
84Dic61C22⋊C811yescharacteristic
85C2×#349—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—41no—
88C2×C61C2×C22⋊C811yescharacteristic
89D61—21no—
90D61—41no—
91D61#34912yescomplemented
92C22×M16—611no—
93C2×M32—612no—
94#349—612no—
95#349—612no—
96C61C2×#34911yescharacteristic, complemented, Sylow
97C23×C4—611no—
98C2×M16—611no—
99C2×M16—611no—
100C2×M16—611no—
101C2×M16—1222no—
102C2×M16—1222no—
103C2×M16#692311yescharacteristic
104C22×C8—611no—
105C22×C8—611no—
106M32—614no—
107M32—1222no—
108C2×C16—1222no—
109C24—611no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4—611no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4—1221no—
116C22×C4—1221no—
117C22×C4—1221no—
118C22×C4—1221no—
119C22×C4C2×#692311yescharacteristic
120M16—22no—
121M16—1222no—
122M16—1222no—
123M16—1222no—
124C2×C8—611no—
125C2×C8—612no—
126C2×C8—612no—
127C2×C8—611no—
128C2×C8—1221no—
129C2×C8—1221no—
130C2×C8C2×#692311yescharacteristic
131C2×C8C2×#692311yescharacteristic
132C16—1224no—
133C23—611no—
134C23—611no—
135C23—1221no—
136C23—1221no—
137C23—2442no—
138C23D61⋊C811yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—611no—
142C2×C4—611no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4D61⋊C811yescharacteristic
156C2×C4C22×#692311yescharacteristic
157C8—21no—
158C8—612no—
159C8—1221no—
160C8C22⋊#692312yes—
161C22—21no—
162C22—41no—
163C22—611no—
164C22—611no—
165C22—1222no—
166C22—1221no—
167C22—2441no—
168C22—2442no—
169C22—2442no—
170C22C2×D61⋊C811yescharacteristic
171C4—21no—
172C4—611no—
173C4—611no—
174C4—1221no—
175C4C2×C22⋊#692311yescharacteristic
176C4D61⋊M1611yescharacteristic
177C2—21no—
178C2—41no—
179C2—612no—
180C2—1221no—
181C2—2441no—
182C2D61⋊(C22⋊C8)11yescharacteristic
subgroupG/H
centerC4C2×C22⋊#6923
commutatorC22×C61C22×C8
FrattiniC2×C4C22×#6923
FittingC2×M16×C61C4
socleC2×C61C2×C22⋊C8
hypercenterC2×M16#6923
hypocenterC61C2×#349
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. D61⋊M32C2semidirect
2. #16840659C2semidirect
3. #16840658C2semidirect
6. #14519851C22semidirect
91. D61#349semidirect
96. C61C2×#349semidirect