Finite Group Databasebeta

← D61⋊#354 #21462088

Subgroups — D61⋊#354 #21462088

Order 7808.

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

normal subgroups only

This group has 284 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⋊#99C212yesmaximal
2#16840669C212yesmaximal, complemented
3#16840668C212yesmaximal, complemented
4#124×D61C211yesmaximal, characteristic
5C2×C22⋊#6923—22no—
6#14519836C2214yes—
7#14519835—22no—
8C2×Q8×D61C411yescharacteristic, complemented
9C2×D4×D61C2211yescharacteristic
10#14519766C2211yescharacteristic
11#14519765C2211yescharacteristic
12#14519764C411yescharacteristic, complemented
13#14519763—22no—
14C22⋊C4×D61—22no—
15C42×D61C411yescharacteristic, complemented
16#124×C61C411yescharacteristic, complemented
17C23×D61D412yes—
18C22×#6923—42no—
19C2×Q8×C61C2×C411yescharacteristic, complemented
20C2×D4×C61C2×C411yescharacteristic
21C2×C22⋊D61D412yes—
22Q8×D61—41no—
23Q8×D61—41no—
24D4×D61—41no—
25D4×D61—41no—
26C2×D244C2311yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61—21no—
29C2×C4×D61C2×C411yescharacteristic
30C2×Dic122—21no—
31C2×Dic122C2×C411yescharacteristic, complemented
32C22⋊#6923—24no—
33C22⋊#6923—42no—
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic, complemented
36C22⋊Dic61—22no—
37#11758198—22no—
38#11758198—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic, complemented
41C23×C61C22⋊C412yes—
42C22×D61—22no—
43C22×D61—22no—
44C22×D61—44no—
45C22×D61C22⋊C411yescharacteristic
46C22×D61C2×D412yes—
47C2×#6923—44no—
48C2×#6923—84no—
49Q8×C61—41no—
50D4×C61—41no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61C22×C411yescharacteristic
54C22⋊D61—42no—
55C2×Dic61—21no—
56C2×Dic61—21no—
57C2×Dic61C22⋊C411yescharacteristic
58D244—41no—
59C4×D61—21no—
60C4×D61—21no—
61C4×D61—42no—
62C4×D61—41no—
63C4×D61—41no—
64Dic122—42no—
65Dic122—41no—
66C22×C61—22no—
67C22×C61—42no—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—22no—
70C2×D61—22no—
71C2×D61—44no—
72C2×D61—42no—
73C2×D61—82no—
74C2×D61#9911yescharacteristic
75C2×D61#9911yescharacteristic
76#6923—84no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80Dic61—21no—
81Dic61—41no—
82Dic61—41no—
83C2×#354—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—42no—
86C2×C61C2×#9911yescharacteristic
87D61—21no—
88D61—42no—
89D61#35412yescomplemented
90C2×#124—611no—
91C2×#99—612no—
92#354—612no—
93#354—612no—
94C61C2×#35411yescharacteristic, complemented, Sylow
95C22×Q8—611no—
96C22×D4—611no—
97#124—611no—
98#124—611no—
99#124—611no—
100#124—1222no—
101#124#692311yescharacteristic, complemented
102C2×C22⋊C4—1222no—
103C2×C22⋊C4—1222no—
104C2×C42—611no—
105#99—614no—
106#99—1222no—
107C24—612no—
108C2×Q8—611no—
109C2×Q8—1221no—
110C2×Q8—2441no—
111C2×Q8—2441no—
112C2×Q8C2×#692311yescharacteristic, complemented
113C2×D4—612no—
114C2×D4—611no—
115C2×D4—2441no—
116C2×D4—2441no—
117C2×D4C2×#692311yescharacteristic
118C22×C4—611no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4—2442no—
122C22⋊C4—22no—
123C22⋊C4—1222no—
124C22⋊C4—1222no—
125C22⋊C4—1222no—
126C22⋊C4—1224no—
127C22⋊C4—2442no—
128C42—611no—
129C42—1221no—
130C42C2×#692311yescharacteristic, complemented
131C23—611no—
132C23—612no—
133C23—1222no—
134C23—1222no—
135C23—2444no—
136C23C22⋊#692312yes—
137Q8—41no—
138Q8—2441no—
139Q8—2442no—
140D4—41no—
141D4—2441no—
142D4—2442no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—611no—
146C2×C4—1221no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—4884no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4—2442no—
154C2×C4—2444no—
155C2×C4C22×#692311yescharacteristic
156C22—22no—
157C22—42no—
158C22—611no—
159C22—611no—
160C22—1222no—
161C22—1222no—
162C22—4882no—
163C22—2442no—
164C22—2444no—
165C22C2×C22⋊#692311yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—1221no—
170C4—4884no—
171C4—2441no—
172C4—2441no—
173C2—21no—
174C2—42no—
175C2—612no—
176C2—1221no—
177C2—2442no—
178C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61C2×#99
hypercenter#124#6923
hypocenterC61C2×#354
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #16840669C2semidirect
3. #16840668C2semidirect
8. C2×Q8×D61C4semidirect
12. #14519764C4semidirect
15. C42×D61C4semidirect
16. #124×C61C4semidirect
19. C2×Q8×C61C2×C4semidirect
31. C2×Dic122C2×C4semidirect
35. C42×C61C2×C4semidirect
40. C4×Dic61C2×C4semidirect
89. D61#354semidirect
94. C61C2×#354semidirect
101. #124#6923semidirect
112. C2×Q8C2×#6923semidirect
130. C42C2×#6923semidirect