Finite Group Databasebeta

← #21461845

Subgroups — #21461845

Order 7808.

390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×#14519837C212yesmaximal, complemented
3#16840734C211yesmaximal, characteristic, complemented
4#16840642C212yesmaximal, complemented
5C2×#14519750C211yesmaximal, characteristic
6C2×#11758213—21no—
7D61⋊M16—24no—
8C2×#11758217C2212yes—
9C2×#11758217C2212yes—
10C2×D61⋊C8—21no—
11#14519837—24no—
12#14519834—21no—
13#14519834—21no—
14C22×D244C411yescharacteristic
15C22×C22⋊D61C411yescharacteristic
16C22×C22⋊D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519750—21no—
19#14519750—21no—
20#14519750—21no—
21#14519750—21no—
22C2×#11758196C2211yescharacteristic
23C2×#11758198C411yescharacteristic
24C2×C22⋊C4×C61C411yescharacteristic
25C24×C61C2×C411yescharacteristic
26C23×D61C2×C411yescharacteristic
27C23×D61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×C22⋊D61—22no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—22no—
36C2×C22⋊D61—42no—
37C22×Dic61C2×C411yescharacteristic
38C22×Dic61C2311yescharacteristic
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—42no—
42C2×C4×D61—22no—
43C2×C4×D61—22no—
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61D411yescharacteristic
48#11758217—22no—
49#11758217—22no—
50#11758217—22no—
51#11758217D414yescomplemented
52C2×#92420—22no—
53C2×#92420—22no—
54#11758213—24no—
55D61⋊C8—24no—
56C22⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58#11758198—21no—
59#11758198—21no—
60#11758196—21no—
61#11758196—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61C22×C411yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—21no—
70C22×D61—22no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61C22⋊C411yescharacteristic
75C22×D61C22⋊C411yescharacteristic
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61C22⋊C411yescharacteristic
80C2×C4×C61C22⋊C411yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—42no—
83C22⋊D61—41no—
84C22⋊D61—42no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D411yescharacteristic
90C2×Dic61C2×D411yescharacteristic
91C2×Dic61#4112yes—
92D244—42no—
93D244—42no—
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—21no—
99C4×D61—21no—
100#92420—24no—
101#92420—42no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—82no—
108C22×C61C2×C22⋊C411yescharacteristic
109C22×C61C4×D412yes—
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—21no—
115C2×D61—44no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—82no—
120C2×D61#10012yescomplemented
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—41no—
124Dic61—41no—
125Dic61#12011yescharacteristic
126Dic61#12112yes—
127Dic61#12311yescharacteristic
128#1900—611nomaximal, Sylow
129C2×C61—22no—
130C2×C61—81no—
131C2×C61#38611yescharacteristic
132C2×C61C2×#10011yescharacteristic
133C2×C61#41311yescharacteristic
134D61—22no—
135D61—41no—
136D61—81no—
137C22×M16—611no—
138C2×#121—611no—
139C2×#100—612no—
140#407—611no—
141#343—612no—
142C61#190011yescharacteristic, complemented, Sylow
143C22×D4—611no—
144C22×D4—611no—
145C22×D4—611no—
146C23×C4—611no—
147C2×M16—612no—
148C2×M16—612no—
149C2×M16—1224no—
150C2×M16—1221no—
151C22×C8—1221no—
152#121—1221no—
153#121—1221no—
154#121—1221no—
155#121—1221no—
156C2×C4⋊C4—611no—
157C2×C22⋊C4—611no—
158C2×C22⋊C4#692311yescharacteristic
159#100—1224no—
160C22⋊C8—1221no—
161C22⋊C8—1221no—
162C24—611no—
163C24—611no—
164C24C2×#692311yescharacteristic
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1222no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1222no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—2442no—
174C2×D4—2442no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4C2×#692311yescharacteristic
184C22×C4C2×#692311yescharacteristic
185M16—614no—
186M16—1222no—
187M16—1224no—
188M16—1222no—
189M16—1222no—
190C2×C8—1222no—
191C2×C8—1224no—
192C2×C8—1222no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C23—21no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—611no—
204C23—611no—
205C23—1222no—
206C23—1222no—
207C23—1222no—
208C23—1221no—
209C23—2441no—
210C23—2441no—
211C23—2441no—
212C23C22×#692311yescharacteristic
213D4—2442no—
214D4—2442no—
215D4—2441no—
216D4—2442no—
217D4—2441no—
218D4—2442no—
219D4—2442no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—612no—
226C2×C4—612no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2441no—
235C2×C4C22⋊#692311yescharacteristic
236C2×C4C22⋊#692311yescharacteristic
237C8—1224no—
238C8—2442no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—612no—
246C22—1221no—
247C22—1221no—
248C22—1221no—
249C22—1221no—
250C22—1221no—
251C22—4882no—
252C22—2444no—
253C22—2441no—
254C22—2441no—
255C22—2441no—
256C22C2×C22⋊#692311yescharacteristic
257C22D4×#692312yes—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—611no—
262C4—612no—
263C4—611no—
264C4—2441no—
265C2—22no—
266C2—81no—
267C2—1222no—
268C2—4881no—
269C2—2441no—
270C2#1684071011yescharacteristic
271C2D61⋊#10011yescharacteristic
272C2#1684074811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1900
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊M16C2semidirect
2. C2×#14519837C2semidirect
3. #16840734C2semidirect
4. #16840642C2semidirect
51. #11758217D4semidirect
120. C2×D61#100semidirect
142. C61#1900semidirect