Finite Group Databasebeta

← D61⋊#353 #21462085

Subgroups — D61⋊#353 #21462085

Order 7808.

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

normal subgroups only

This group has 368 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, complemented
2#16840667C212yesmaximal, complemented
3#16840666C212yesmaximal, complemented
4#127×D61C211yesmaximal, characteristic
5C2×C22⋊#6923—22no—
6#14519836C2214yescomplemented
7#14519835—22no—
8C2×D4×D61—22no—
9C2×D4×D61C411yescharacteristic, complemented
10C2×D4×D61C2211yescharacteristic
11#14519774C2211yescharacteristic
12#14519773—22no—
13#14519773C411yescharacteristic, complemented
14#14519773C2211yescharacteristic
15C42×D61C411yescharacteristic, complemented
16#127×C61C411yescharacteristic, complemented
17C23×D61—21no—
18C23×D61D412yes—
19C22×#6923—42no—
20C2×D4×C61—22no—
21C2×D4×C61C2×C411yescharacteristic
22C2×D4×C61C2×C411yescharacteristic, complemented
23C2×C22⋊D61—22no—
24C2×C22⋊D61—22no—
25C2×C22⋊D61—21no—
26C2×C22⋊D61D412yes—
27D4×D61—41no—
28D4×D61—41no—
29D4×D61—48no—
30D4×D61—41no—
31D4×D61—41no—
32C2×D244—22no—
33C2×D244C2×C411yescharacteristic, complemented
34C2×D244C2311yescharacteristic
35C2×C4×D61—21no—
36C2×C4×D61C2×C411yescharacteristic
37C22⋊#6923—24no—
38C22⋊#6923—42no—
39C42×C61C2×C411yescharacteristic, complemented
40C4×Dic61—21no—
41C4×Dic61C2×C411yescharacteristic, complemented
42C23×C61—21no—
43C23×C61C22⋊C412yes—
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—21no—
47C22×D61—44no—
48C22×D61—44no—
49C22×D61—41no—
50C22×D61—41no—
51C22×D61C22⋊C411yescharacteristic
52C22×D61C2×D412yes—
53C2×#6923—44no—
54C2×#6923—84no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—44no—
58C2×C4×C61—21no—
59C2×C4×C61C22×C411yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—44no—
62C22⋊D61—44no—
63C22⋊D61—42no—
64C2×Dic61—21no—
65C2×Dic61C22⋊C411yescharacteristic
66D244—41no—
67D244—41no—
68D244—44no—
69C4×D61—24no—
70C4×D61—21no—
71C4×D61—21no—
72C22×C61—22no—
73C22×C61—42no—
74C22×C61—42no—
75C22×C61—41no—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—22no—
78C2×D61—22no—
79C2×D61—44no—
80C2×D61—42no—
81C2×D61—42no—
82C2×D61—41no—
83C2×D61—82no—
84C2×D61—82no—
85C2×D61—82no—
86C2×D61#9911yescharacteristic
87C2×D61#9911yescharacteristic
88#6923—84no—
89C4×C61—22no—
90C4×C61—21no—
91Dic61—22no—
92Dic61—21no—
93C2×#353—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—42no—
96C2×C61—81no—
97C2×C61C2×#9911yescharacteristic
98D61—21no—
99D61—42no—
100D61—81no—
101D61#35312yescomplemented
102C2×#127—611no—
103C2×#99—612no—
104#353—612no—
105#353—612no—
106C61C2×#35311yescharacteristic, complemented, Sylow
107C22×D4—611no—
108C22×D4—611no—
109C22×D4—1222no—
110#127—611no—
111#127—611no—
112#127—611no—
113#127—1222no—
114#127#692311yescharacteristic, complemented
115C2×C22⋊C4—1222no—
116C2×C42—611no—
117#99—614no—
118#99—1222no—
119C24—612no—
120C24—1221no—
121C2×D4—22no—
122C2×D4—612no—
123C2×D4—611no—
124C2×D4—611no—
125C2×D4—1222no—
126C2×D4—1221no—
127C2×D4—1222no—
128C2×D4—1222no—
129C2×D4—2441no—
130C2×D4—2441no—
131C2×D4—2441no—
132C2×D4—2441no—
133C2×D4—2448no—
134C2×D4C2×#692311yescharacteristic
135C2×D4C2×#692311yescharacteristic, complemented
136C22×C4—611no—
137C22×C4—1221no—
138C22×C4—2442no—
139C22⋊C4—1224no—
140C22⋊C4—2442no—
141C42—611no—
142C42—1221no—
143C42C2×#692311yescharacteristic, complemented
144C23—21no—
145C23—611no—
146C23—612no—
147C23—1222no—
148C23—1222no—
149C23—1221no—
150C23—2441no—
151C23—2441no—
152C23—2444no—
153C23—2444no—
154C23C22⋊#692312yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—2441no—
159D4—2441no—
160D4—2444no—
161D4—2442no—
162D4—2444no—
163D4—2444no—
164D4—2442no—
165C2×C4—21no—
166C2×C4—611no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1224no—
170C2×C4—1221no—
171C2×C4—4884no—
172C2×C4—2444no—
173C2×C4C22×#692311yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—611no—
179C22—611no—
180C22—1222no—
181C22—1222no—
182C22—4882no—
183C22—4882no—
184C22—4882no—
185C22—2442no—
186C22—2442no—
187C22—2444no—
188C22—2441no—
189C22C2×C22⋊#692311yescharacteristic
190C4—22no—
191C4—21no—
192C4—1222no—
193C4—1221no—
194C4—4884no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—612no—
199C2—1221no—
200C2—4881no—
201C2—2442no—
202C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC2×C61C2×#99
hypercenter#127#6923
hypocenterC61C2×#353
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D61⋊#99C2semidirect
2. #16840667C2semidirect
3. #16840666C2semidirect
6. #14519836C22semidirect
9. C2×D4×D61C4semidirect
13. #14519773C4semidirect
15. C42×D61C4semidirect
16. #127×C61C4semidirect
22. C2×D4×C61C2×C4semidirect
33. C2×D244C2×C4semidirect
39. C42×C61C2×C4semidirect
41. C4×Dic61C2×C4semidirect
101. D61#353semidirect
106. C61C2×#353semidirect
114. #127#6923semidirect
135. C2×D4C2×#6923semidirect
143. C42C2×#6923semidirect