Finite Group Databasebeta

← D61⋊#355 #21462105

Subgroups — D61⋊#355 #21462105

Order 7808.

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

normal subgroups only

This group has 260 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
1D61⋊#101C212yesmaximal, complemented
2#16840671C212yesmaximal, complemented
3#16840670C212yesmaximal, complemented
4#124×D61C211yesmaximal, characteristic
5D61⋊M16—22no—
6#14519838—22no—
7#14519838C2214yescomplemented
8C2×Q8×D61C2211yescharacteristic
9C2×D4×D61C411yescharacteristic
10#14519766C411yescharacteristic
11#14519765C2211yescharacteristic
12#14519764C2211yescharacteristic
13#14519763—22no—
14C22⋊C4×D61—22no—
15C42×D61C411yescharacteristic
16#124×C61C411yescharacteristic
17C23×D61—21no—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61C2×C411yescharacteristic
20C2×C22⋊D61—21no—
21Q8×D61—41no—
22Q8×D61—41no—
23D4×D61—41no—
24D4×D61—41no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D412yes—
29C2×Dic122D412yes—
30C2×Dic122C2311yescharacteristic
31#11758217—24no—
32#11758213—42no—
33D61⋊C8—42no—
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—22no—
37#11758198—22no—
38#11758198—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41C23×C61—21no—
42C22×D61—21no—
43C22×D61—44no—
44C22×D61—41no—
45C22×D61—41no—
46C22×D61C22⋊C411yescharacteristic
47Q8×C61—41no—
48D4×C61—41no—
49C2×C4×C61—21no—
50C2×C4×C61C22⋊C412yes—
51C2×C4×C61C22×C411yescharacteristic
52C22⋊D61—42no—
53C2×Dic61—21no—
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C2×D412yes—
56D244—41no—
57C4×D61—22no—
58C4×D61—22no—
59C4×D61—21no—
60C4×D61—21no—
61C4×D61—42no—
62Dic122—42no—
63Dic122—41no—
64#92420—44no—
65C22×C61—42no—
66C22×C61—41no—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—22no—
69C2×D61—42no—
70C2×D61—41no—
71C2×D61—82no—
72C2×D61—82no—
73C2×D61#9911yescharacteristic
74C2×D61#9911yescharacteristic
75C4×C61—21no—
76C4×C61—22no—
77C4×C61—41no—
78Dic61—22no—
79Dic61—21no—
80Dic61—41no—
81C2×#355—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—81no—
84C2×C61C2×#9911yescharacteristic
85D61—21no—
86D61—81no—
87D61#35512yescomplemented
88C2×#124—611no—
89C2×#101—612no—
90#355—612no—
91#355—612no—
92C61C2×#35511yescharacteristic, complemented, Sylow
93C22×Q8—611no—
94C22×D4—611no—
95C2×M16—1222no—
96#124—611no—
97#124—611no—
98#124—611no—
99#124—1222no—
100#124#692311yescharacteristic
101C2×C22⋊C4—1222no—
102C2×C42—611no—
103#101—614no—
104#101—1222no—
105C24—1221no—
106C2×Q8—612no—
107C2×Q8—611no—
108C2×Q8—2441no—
109C2×Q8—2441no—
110C2×Q8C2×#692311yescharacteristic
111C2×D4—611no—
112C2×D4—1221no—
113C2×D4—2441no—
114C2×D4—2441no—
115C2×D4C2×#692311yescharacteristic
116C22×C4—612no—
117C22×C4—611no—
118C22×C4—1221no—
119M16—1224no—
120M16—2442no—
121C2×C8—2442no—
122C22⋊C4—22no—
123C22⋊C4—1222no—
124C22⋊C4—1222no—
125C22⋊C4—1222no—
126C42—611no—
127C42—1221no—
128C42C2×#692311yescharacteristic
129C23—21no—
130C23—611no—
131C23—1221no—
132C23—2441no—
133C23—2441no—
134C23—2444no—
135Q8—41no—
136Q8—2442no—
137Q8—2441no—
138D4—41no—
139D4—2441no—
140D4—2442no—
141C2×C4—21no—
142C2×C4—611no—
143C2×C4—612no—
144C2×C4—1222no—
145C2×C4—1222no—
146C2×C4—1221no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—2442no—
150C2×C4C22⋊#692312yes—
151C2×C4C22×#692311yescharacteristic
152C8—2444no—
153C22—42no—
154C22—41no—
155C22—611no—
156C22—611no—
157C22—1222no—
158C22—4882no—
159C22—4882no—
160C22—2442no—
161C22—2441no—
162C22C2×C22⋊#692311yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—1222no—
167C4—1221no—
168C4—2441no—
169C2—21no—
170C2—81no—
171C2—612no—
172C2—1221no—
173C2—4881no—
174C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61C2×#99
hypercenter#124#6923
hypocenterC61C2×#355
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D61⋊#101C2semidirect
2. #16840671C2semidirect
3. #16840670C2semidirect
7. #14519838C22semidirect
87. D61#355semidirect
92. C61C2×#355semidirect