Finite Group Databasebeta

← D61⋊#352 #21462068

Subgroups — D61⋊#352 #21462068

Order 7808.

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

normal subgroups only

This group has 278 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⋊#100C211yesmaximal, characteristic
2D61⋊#99C211yesmaximal, characteristic
3#16840665C212yesmaximal, complemented
4#16840664C212yesmaximal, complemented
5#123×D61C211yesmaximal, characteristic
6D61⋊M16—21no—
7C2×C22⋊#6923—21no—
8#14519837—21no—
9#14519837C2212yes—
10#14519836—21no—
11#14519835C2212yes—
12C2×D4×D61C2211yescharacteristic
13C22×C4×D61C411yescharacteristic, complemented
14#14519762—21no—
15#14519761C2211yescharacteristic
16#14519760C2211yescharacteristic
17#14519759—21no—
18#14519758C411yescharacteristic, complemented
19C4⋊C4×D61—21no—
20C22⋊C4×D61—21no—
21C22⋊C4×D61C411yescharacteristic, complemented
22#123×C61C411yescharacteristic, complemented
23C23×D61C2×C411yescharacteristic
24C23×D61D411yescharacteristic
25C22×#6923—41no—
26C2×D4×C61C2×C411yescharacteristic
27C22×C4×C61C2×C411yescharacteristic, complemented
28C2×C22⋊D61D411yescharacteristic
29C2×C22⋊D61C2311yescharacteristic
30C22×Dic61C2×C411yescharacteristic, complemented
31D4×D61—41no—
32D4×D61—41no—
33C2×D244D411yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—21no—
37C2×C4×D61—41no—
38C2×C4×D61—41no—
39C2×C4×D61D411yescharacteristic
40C22⋊#6923—22no—
41C22⋊#6923—41no—
42#11758217—22no—
43#11758213—41no—
44D61⋊C8—41no—
45C4⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61C2×C411yescharacteristic, complemented
48C22⋊Dic61—21no—
49C22⋊Dic61C2×C411yescharacteristic, complemented
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53C4⋊Dic61—21no—
54#11758196—21no—
55#11758196—21no—
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61C22⋊C411yescharacteristic
65C22×D61C22⋊C411yescharacteristic
66C22×D61C2×D411yescharacteristic
67C2×#6923—42no—
68C2×#6923—82no—
69D4×C61—41no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61C22⋊C411yescharacteristic
74C22⋊D61—41no—
75C22⋊D61—41no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61C2×D411yescharacteristic
80D244—41no—
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—42no—
84C4×D61—42no—
85C4×D61—41no—
86C4×D61—41no—
87#92420—42no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C2×C22⋊C411yescharacteristic
93C2×D61—22no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—81no—
102C2×D61#9911yescharacteristic
103C2×D61#9911yescharacteristic
104#6923—82no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—41no—
108Dic61—21no—
109Dic61—41no—
110Dic61—41no—
111C2×#352—611nomaximal, Sylow
112C2×C61—21no—
113C2×C61—41no—
114C2×C61—41no—
115C2×C61C2×#9911yescharacteristic
116D61—21no—
117D61—41no—
118D61—41no—
119D61#35212yescomplemented
120C2×#123—611no—
121C2×#100—611no—
122C2×#99—611no—
123#352—612no—
124#352—612no—
125C61C2×#35211yescharacteristic, complemented, Sylow
126C22×D4—611no—
127C23×C4—611no—
128C2×M16—1221no—
129#123—611no—
130#123—611no—
131#123—611no—
132#123—1221no—
133#123—1221no—
134#123#692311yescharacteristic, complemented
135C2×C4⋊C4—1221no—
136C2×C22⋊C4—611no—
137C2×C22⋊C4—1221no—
138C2×C22⋊C4—1221no—
139#100—612no—
140#100—1221no—
141#99—612no—
142#99—1221no—
143C24—611no—
144C24—611no—
145C2×D4—611no—
146C2×D4—611no—
147C2×D4—611no—
148C2×D4—2441no—
149C2×D4—2441no—
150C2×D4C2×#692311yescharacteristic
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—1221no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—2441no—
157C22×C4—2441no—
158C22×C4—2441no—
159C22×C4C2×#692311yescharacteristic, complemented
160M16—1222no—
161M16—2441no—
162C2×C8—2441no—
163C4⋊C4—21no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C22⋊C4—21no—
168C22⋊C4—611no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1222no—
174C22⋊C4—2441no—
175C22⋊C4C2×#692311yescharacteristic, complemented
176C23—611no—
177C23—611no—
178C23—611no—
179C23—1221no—
180C23—1221no—
181C23—1221no—
182C23—1221no—
183C23—2442no—
184C23—2442no—
185C23C22⋊#692311yescharacteristic
186C23C22×#692311yescharacteristic
187D4—41no—
188D4—2441no—
189D4—2441no—
190D4—2441no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—4882no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4C22⋊#692311yescharacteristic
207C8—2442no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—611no—
213C22—611no—
214C22—1222no—
215C22—1221no—
216C22—1221no—
217C22—4881no—
218C22—2441no—
219C22—2441no—
220C22—2442no—
221C22—2442no—
222C22—2442no—
223C22C2×C22⋊#692311yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—1221no—
228C4—4882no—
229C4—2441no—
230C4—2441no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—612no—
235C2—1221no—
236C2—2441no—
237C2—2441no—
238C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#123×C61C4
socleC2×C61C2×#99
hypercenter#123#6923
hypocenterC61C2×#352
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #16840665C2semidirect
4. #16840664C2semidirect
13. C22×C4×D61C4semidirect
18. #14519758C4semidirect
21. C22⋊C4×D61C4semidirect
22. #123×C61C4semidirect
27. C22×C4×C61C2×C4semidirect
30. C22×Dic61C2×C4semidirect
47. C22⋊C4×C61C2×C4semidirect
49. C22⋊Dic61C2×C4semidirect
119. D61#352semidirect
125. C61C2×#352semidirect
134. #123#6923semidirect
159. C22×C4C2×#6923semidirect
175. C22⋊C4C2×#6923semidirect