Finite Group Databasebeta

← #21450750

Subgroups — #21450750

Order 7808.

900 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14519760C212yesmaximal, complemented
2C2×#14519751C211yesmaximal, characteristic, complemented
3C2×#14519746C212yesmaximal, complemented
4#16839698C212yesmaximal, complemented
5#16839671C212yesmaximal, complemented
6#16839662C214yesmaximal, complemented
7C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic, complemented
10C22×C22⋊D61C2212yes—
11C22×C22⋊D61C2214yes—
12#14519760—28no—
13#14519751—24no—
14#14519746—28no—
15C2×C4⋊Dic61C2211yescharacteristic, complemented
16C2×#11758196C2214yescomplemented
17C2×C22⋊Dic61C2214yes—
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2212yescomplemented
20C2×#11758198C2214yescomplemented
21C2×C4×Dic61C2212yescomplemented
22#14519684C2212yescomplemented
23C25×C61C2211yescharacteristic
24C23×C4×C61C2211yescharacteristic
25C23×C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61—24no—
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2212yes—
29C24×C61—22no—
30C24×C61—24no—
31C24×C61—24no—
32C24×C61—42no—
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35C23×D61C2312yes—
36C22×C4×C61—22no—
37C22×C4×C61—24no—
38C22×C4×C61—42no—
39C22×C4×C61D414yescomplemented
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—28no—
47C2×C22⋊D61—28no—
48C2×C22⋊D61—44no—
49C22×Dic61C2312yes—
50C22×Dic61C2314yes—
51C2×D244—22no—
52C2×D244—42no—
53C22⋊C4×C61—24no—
54C22⋊C4×C61—24no—
55C22⋊Dic61—28no—
56C22⋊Dic61D418yescomplemented
57#11758198—24no—
58#11758198—28no—
59C4⋊Dic61—22no—
60#11758196—28no—
61C4×Dic61—42no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—28no—
65C23×C61—24no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—24no—
69C23×C61—416no—
70C23×C61—44no—
71C23×C61—44no—
72C23×C61C2×D414yes—
73C23×C61C2×D412yes—
74C23×C61#4114yes—
75C23×C61C2411yescharacteristic
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—24no—
80C22×D61—24no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—24no—
84C2×C4×C61—22no—
85C2×C4×C61—44no—
86C2×C4×C61—44no—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×D412yes—
89C22⋊D61—416no—
90C22⋊D61—48no—
91C2×Dic61—24no—
92C2×Dic61—24no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61C2×D418yes—
97D244—44no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—28no—
101C22×C61—24no—
102C22×C61—28no—
103C22×C61—416no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—44no—
107C22×C61#12714yes—
108C22×C61C22×D412yes—
109C22×C61C22×D411yescharacteristic
110C22×C61C2×#4112yes—
111C22×C61H(5,𝔽2)12yes—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—44no—
116C2×D61—44no—
117C4×C61—22no—
118C4×C61—22no—
119C4×C61—42no—
120Dic61—28no—
121Dic61—42no—
122#2539—611nomaximal, Sylow
123C2×C61—24no—
124C2×C61—44no—
125C2×C61#52511yescharacteristic
126C2×C61C2×#12711yescharacteristic
127C2×C61#53411yescharacteristic
128C2×C61#54614yes—
129D61—82no—
130C2×#123—612no—
131C2×#121—611no—
132C2×#120—612no—
133C22×C22⋊C4D6111yescharacteristic, complemented
134#399—612no—
135#392—612no—
136#390—614no—
137C4×C22⋊C4—611no—
138C61#253911yescharacteristic, complemented, Sylow
139C25C2×D6111yescharacteristic
140C22×D4—612no—
141C22×D4—614no—
142C22×D4—611no—
143C23×C4C2×D6111yescharacteristic
144C23×C4C2×D6111yescharacteristic
145#123—1228no—
146#121—1224no—
147#120—1228no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—614no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—614no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4—614no—
155C2×C22⋊C4C2×D6112yes—
156C2×C22⋊C4C2×D6112yes—
157C2×C42—612no—
158#95—612no—
159C24—24no—
160C24—22no—
161C24—24no—
162C24—42no—
163C24—612no—
164C24C22×D6112yes—
165C24C22×D6111yescharacteristic
166C2×D4—1228no—
167C2×D4—1228no—
168C2×D4—1224no—
169C2×D4—1224no—
170C2×D4—1224no—
171C2×D4—1222no—
172C2×D4—2442no—
173C2×D4—2444no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—42no—
177C22×C4—614no—
178C22×C4—612no—
179C22×C4C22⋊D6114yescomplemented
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—1228no—
184C4⋊C4—1222no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C22⋊C4—618no—
188C22⋊C4—1228no—
189C22⋊C4—1228no—
190C22⋊C4—1224no—
191C42—2442no—
192C23—22no—
193C23—22no—
194C23—28no—
195C23—24no—
196C23—22no—
197C23—22no—
198C23—24no—
199C23—416no—
200C23—44no—
201C23—44no—
202C23—1222no—
203C23—1222no—
204C23—1222no—
205C23—1224no—
206C23—1224no—
207C23#1175822214yes—
208C23D4×D6114yes—
209C23C2×C22⋊D6112yes—
210C23C23×D6111yescharacteristic
211D4—2444no—
212D4—24416no—
213D4—2448no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—618no—
221C2×C4—1224no—
222C2×C4—1224no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4C2×C22⋊D6112yes—
227C2×C4C2×C22⋊D6112yes—
228C22—22no—
229C22—22no—
230C22—28no—
231C22—24no—
232C22—28no—
233C22—416no—
234C22—42no—
235C22—42no—
236C22—44no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2444no—
241C22—2444no—
242C22#1451977314yes—
243C22C2×D4×D6112yes—
244C22C22×C22⋊D6111yescharacteristic
245C22C2×#1175822212yes—
246C22#1451982212yes—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—1228no—
251C4—2442no—
252C2—24no—
253C2—44no—
254C2—4882no—
255C2#1684027311yescharacteristic
256C2C2×#1451977311yescharacteristic
257C2#1684032111yescharacteristic
258C2#1684040214yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C22⋊C4×C61C2
hypercenterC22×C22⋊C4D61
hypocenterC61#2539
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
2. C2×#14519751C2semidirect
3. C2×#14519746C2semidirect
4. #16839698C2semidirect
5. #16839671C2semidirect
6. #16839662C2semidirect
7. C4×C22⋊Dic61C2semidirect
8. C22×C22⋊C4×C61C2semidirect
9. C22×D244C22semidirect
15. C2×C4⋊Dic61C22semidirect
16. C2×#11758196C22semidirect
19. C2×#11758198C22semidirect
20. C2×#11758198C22semidirect
21. C2×C4×Dic61C22semidirect
22. #14519684C22semidirect
39. C22×C4×C61D4semidirect
56. C22⋊Dic61D4semidirect
133. C22×C22⋊C4D61semidirect
138. C61#2539semidirect
179. C22×C4C22⋊D61semidirect