Finite Group Databasebeta

← #21461869

Subgroups — #21461869

Order 7808.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#16840829C211yesmaximal, characteristic, complemented
2C2×#14519836C212yesmaximal, complemented
3D61⋊#99C211yesmaximal, characteristic, complemented
4#16840639C212yesmaximal, complemented
5#16840323C211yesmaximal, characteristic
6D4×#6923—24no—
7#14519856—21no—
8C2×C22⋊#6923—21no—
9C2×C22⋊#6923C2212yes—
10C2×C22⋊#6923C2212yes—
11#14519836—21no—
12#14519836—24no—
13#14519835—21no—
14C22×D244C2211yescharacteristic
15C2×D4×D61C2211yescharacteristic
16#14519762—21no—
17#14519760C411yescharacteristic, complemented
18#14519752—21no—
19#14519750—21no—
20#14519747—21no—
21#14519747C411yescharacteristic, complemented
22#14519745C411yescharacteristic, complemented
23C22⋊C4×D61C2211yescharacteristic
24#123×C61C411yescharacteristic, complemented
25C23×D61C2×C411yescharacteristic, complemented
26C23×D61D411yescharacteristic
27C23×D61C2311yescharacteristic
28C22×#6923—22no—
29C22×#6923—22no—
30C22×#6923—22no—
31C2×D4×C61C2×C411yescharacteristic
32C22×C4×C61C2×C411yescharacteristic, complemented
33C2×C22⋊D61—21no—
34C2×C22⋊D61C2×C411yescharacteristic
35C2×C22⋊D61D411yescharacteristic
36D4×D61—22no—
37D4×D61—22no—
38C2×D244—22no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—22no—
42C2×D244—21no—
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61D411yescharacteristic
46C22⋊#6923—22no—
47C22⋊#6923—22no—
48C22⋊#6923—22no—
49C22⋊#6923—22no—
50C22⋊#6923D414yescomplemented
51C4⋊#6923—22no—
52C4×#6923—22no—
53C4⋊C4×C61—21no—
54C22⋊C4×C61—21no—
55C22⋊C4×C61C2×C411yescharacteristic, complemented
56C22⋊Dic61C2×C411yescharacteristic, complemented
57#11758198—21no—
58#11758198—21no—
59#11758198—21no—
60#11758198—21no—
61#11758196—21no—
62C23×C61C22⋊C411yescharacteristic
63C23×C61C22×C411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—81no—
69C22×D61—81no—
70C22×D61—81no—
71C22×D61C22⋊C411yescharacteristic
72C22×D61C2×D412yes—
73C22×D61C2×D411yescharacteristic
74C22×D61C2×D411yescharacteristic
75C22×D61#4112yes—
76C2×#6923—24no—
77C2×#6923—42no—
78C2×#6923—82no—
79C2×#6923—82no—
80C2×#6923—82no—
81D4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61C22⋊C411yescharacteristic
86C22⋊D61—22no—
87C22⋊D61—22no—
88C22⋊D61—81no—
89C2×Dic61—21no—
90C2×Dic61C22⋊C411yescharacteristic
91D244—22no—
92D244—41no—
93D244—42no—
94D244—41no—
95D244—81no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—81no—
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61C2×C22⋊C411yescharacteristic
103C22×C61C4×D412yes—
104C2×D61—21no—
105C2×D61—41no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—41no—
109C2×D61—42no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—81no—
115C2×D61—82no—
116C2×D61#12011yescharacteristic
117C2×D61#12112yes—
118C2×D61#12311yescharacteristic
119#6923—44no—
120#6923—82no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61—41no—
124Dic61—21no—
125Dic61—41no—
126#1913—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—22no—
129C2×C61—41no—
130C2×C61#38611yescharacteristic
131D61—21no—
132D61—22no—
133D61—21no—
134D61—41no—
135D61—81no—
136#534—611no—
137#518—611no—
138C2×#99—611no—
139C2×#99—612no—
140#342—612no—
141C61#191311yescharacteristic, complemented, Sylow
142C22×D4—611no—
143C22×D4—611no—
144#123—611no—
145#123—1221no—
146#123#692311yescharacteristic, complemented
147#121—1221no—
148#121—1221no—
149#120—611no—
150#120—611no—
151#120—1221no—
152C4×D4—1224no—
153#117—1221no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—611no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—1221no—
158#99—1224no—
159#99—1221no—
160#99—1221no—
161C24—611no—
162C24—611no—
163C24—611no—
164C2×D4—611no—
165C2×D4—611no—
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—1222no—
174C2×D4—1221no—
175C2×D4C2×#692311yescharacteristic
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1222no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4C2×#692311yescharacteristic, complemented
182C4⋊C4—21no—
183C4⋊C4—1221no—
184C4⋊C4—1222no—
185C22⋊C4—21no—
186C22⋊C4—614no—
187C22⋊C4—611no—
188C22⋊C4—1221no—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1221no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4C2×#692311yescharacteristic, complemented
197C42—1222no—
198C23—611no—
199C23—611no—
200C23—612no—
201C23—612no—
202C23—611no—
203C23—1221no—
204C23—1221no—
205C23—1222no—
206C23—1221no—
207C23—4881no—
208C23—4881no—
209C23—4881no—
210C23C22⋊#692311yescharacteristic
211C23C22×#692311yescharacteristic
212D4—22no—
213D4—1222no—
214D4—1222no—
215D4—1222no—
216D4—4881no—
217D4—4881no—
218D4—2441no—
219D4—2441no—
220D4—2442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—611no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1224no—
228C2×C4—1221no—
229C2×C4—4881no—
230C2×C4—4882no—
231C2×C4—4882no—
232C2×C4—4882no—
233C2×C4—2442no—
234C2×C4C22⋊#692311yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—611no—
239C22—611no—
240C22—612no—
241C22—1221no—
242C22—4882no—
243C22—4881no—
244C22—2441no—
245C22—2442no—
246C22—2442no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22—2441no—
251C22—2442no—
252C22—2441no—
253C22C2×C22⋊#692311yescharacteristic
254C22D4×#692312yes—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—1221no—
259C4—4882no—
260C4—2441no—
261C4—2444no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—1222no—
266C2—1221no—
267C2—1221no—
268C2—4881no—
269C2—2441no—
270C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#123×C61C4
socleC2×C61#386
hypercenter#123#6923
hypocenterC61#1913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #16840829C2semidirect
2. C2×#14519836C2semidirect
3. D61⋊#99C2semidirect
4. #16840639C2semidirect
17. #14519760C4semidirect
21. #14519747C4semidirect
22. #14519745C4semidirect
24. #123×C61C4semidirect
25. C23×D61C2×C4semidirect
32. C22×C4×C61C2×C4semidirect
50. C22⋊#6923D4semidirect
55. C22⋊C4×C61C2×C4semidirect
56. C22⋊Dic61C2×C4semidirect
141. C61#1913semidirect
146. #123#6923semidirect
181. C22×C4C2×#6923semidirect
196. C22⋊C4C2×#6923semidirect