Finite Group Databasebeta

← #22620850

Subgroups — #22620850

Order 9344.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989138C211yesmaximal, characteristic, complemented
2#127×D73C211yesmaximal, characteristic, complemented
3#17988964C211yesmaximal, characteristic, complemented
4#17988963C211yesmaximal, characteristic, complemented
5#17988935C211yesmaximal, characteristic, complemented
6#17988781C214yesmaximal, complemented
7#17988722C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#486×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×D4×D73—21no—
12C2×D4×D73—21no—
13C2×D4×D73C2212yes—
14C2×D584C2214yescomplemented
15C2×#11924013C2214yescomplemented
16#14556588C2211yescharacteristic
17#14556588C2211yescharacteristic, complemented
18#14556587—21no—
19#14556587—21no—
20#14556587C2212yes—
21#14556580—21no—
22#14556566—21no—
23#14556566C2212yes—
24#14556553—21no—
25#14556553C2212yescomplemented
26C42×D73C2211yescharacteristic
27#14556520C2212yescomplemented
28#14556511C2214yescomplemented
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic, complemented
31C4⋊Q8×C73C2211yescharacteristic, complemented
32#127×C73C2211yescharacteristic
33#102×C73C2214yescomplemented
34C4×C8×C73C2211yescharacteristic, complemented
35C23×D73—22no—
36#11924029—44no—
37C2×D292—22no—
38C2×D292—21no—
39C2×D292—21no—
40C2×D292—21no—
41C2×D292—21no—
42C2×D292C2312yes—
43C2×D292C2312yes—
44C2×C22⋊D73—22no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—22no—
47D4×D73—44no—
48D4×D73—44no—
49D4×D73—44no—
50C2×C4×D73—22no—
51C2×C4×D73D411yescharacteristic
52C2×C4×D73D411yescharacteristic
53C2×C4×D73C2311yescharacteristic
54D584—44no—
55#11924013—44no—
56C2×#10596831C2312yes—
57#11924005—22no—
58#11924005—22no—
59C4×Dic73D411yescharacteristic
60C4×Dic73D411yescharacteristic
61C4×Dic73C2311yescharacteristic
62C2×Q8×C73—21no—
63C2×D4×C73—21no—
64C2×D4×C73—21no—
65C2×D4×C73C2312yes—
66C2×C8×C73C2312yes—
67C4⋊C4×C73—21no—
68C4⋊C4×C73C2312yes—
69C42×C73C2311yescharacteristic
70C23×C73—22no—
71C22×D73—22no—
72C22×D73—22no—
73C22×D73—44no—
74C22×D73—44no—
75C22×D73—44no—
76C22×D73C2×D411yescharacteristic
77Q8×C73—42no—
78D4×C73—24no—
79D4×C73—42no—
80D4×C73—42no—
81C2×C4×C73—22no—
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2411yescharacteristic
85C22⋊D73—44no—
86C22⋊D73—44no—
87C22⋊D73—44no—
88C2×Dic73C2×D411yescharacteristic
89C2×Dic73C2×D411yescharacteristic
90C2×Dic73C2×D411yescharacteristic
91D292—24no—
92D292—24no—
93D292—44no—
94D292—42no—
95D292—42no—
96D292—42no—
97D292—42no—
98C4×D73—22no—
99C4×D73—22no—
100C4×D73—44no—
101C4×D73D814yescomplemented
102C8×C73—22no—
103#10596831—22no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73C22×D411yescharacteristic
108C2×D73—21no—
109C2×D73—21no—
110C2×D73—42no—
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C2×D73—42no—
115C2×D73—42no—
116C2×D73—88no—
117C2×D73C2×D812yes—
118C4×C73—42no—
119C4×C73C2×D812yes—
120C4×C73AGL(1,ℤ/8)12yes—
121C4×C73H(5,𝔽2)12yes—
122Dic73—21no—
123Dic73—21no—
124Dic73C2×D812yes—
125C2×C73—82no—
126C2×C73#53511yescharacteristic
127C2×C73C22×D811yescharacteristic
128C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
129D73—22no—
130D73—82no—
131D73—82no—
132#3205—731nomaximal, Sylow
133C73#320511yescharacteristic, complemented, Sylow
134#532—731no—
135C2×#127—731no—
136#493—731no—
137#493—731no—
138#486—731no—
139#486D7311yescharacteristic, complemented
140#459—734no—
141#447—734no—
142#431—731no—
143C2×#41—1461no—
144C22×D4—732no—
145C22×D4—1461no—
146C22×D4—1461no—
147C2×D8—734no—
148C2×D8—734no—
149C4⋊Q8C2×D7311yescharacteristic, complemented
150#127—732no—
151#127—731no—
152#127—731no—
153#127—1461no—
154#127—1461no—
155#127C2×D7311yescharacteristic
156#124—1461no—
157#121—732no—
158#121—1461no—
159C4×D4—732no—
160C4×D4—1461no—
161C2×C42—731no—
162C4⋊C8—732no—
163#102—734no—
164#102C2×D7314yescomplemented
165C22⋊C8—732no—
166C4×C8—731no—
167C4×C8C2×D7311yescharacteristic, complemented
168C24—1462no—
169#41—2924no—
170C2×Q8—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—2924no—
174C2×D4—2924no—
175C2×D4—2924no—
176C2×D4—732no—
177C2×D4—732no—
178C2×D4—1462no—
179C2×D4—1462no—
180C2×D4—1462no—
181C2×D4—1462no—
182C2×D4—1461no—
183C2×D4—1461no—
184C2×D4—1461no—
185C2×D4—1461no—
186C2×D4C22×D7312yes—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—731no—
190C22×C4—1462no—
191D8—2924no—
192D8—2924no—
193C2×C8—732no—
194C2×C8C22×D7312yes—
195C4⋊C4—21no—
196C4⋊C4C22×D7312yes—
197C22⋊C4—1462no—
198C22⋊C4—1462no—
199C42—731no—
200C42—731no—
201C42—731no—
202C42C22×D7311yescharacteristic
203C23—22no—
204C23—2924no—
205C23—2924no—
206C23—2924no—
207C23—731no—
208C23—1462no—
209C23—1462no—
210Q8—42no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—2924no—
215D4—2924no—
216D4—2924no—
217D4—2924no—
218D4—2922no—
219D4—2922no—
220D4—2922no—
221D4—2922no—
222D4—1464no—
223D4—1464no—
224C2×C4—22no—
225C2×C4—2924no—
226C2×C4—731no—
227C2×C4—734no—
228C2×C4—731no—
229C2×C4—731no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4D4×D7311yescharacteristic
233C2×C4D4×D7311yescharacteristic
234C2×C4C23×D7311yescharacteristic
235C8—22no—
236C8—1462no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—2922no—
241C22—2922no—
242C22—2922no—
243C22—2922no—
244C22—2922no—
245C22—2922no—
246C22—5848no—
247C22—732no—
248C22—1461no—
249C22—1461no—
250C22C2×D4×D7311yescharacteristic
251C4—42no—
252C4—732no—
253C4—1461no—
254C4—1461no—
255C4D8×D7312yes—
256C4#1455661812yes—
257C4#1455663712yes—
258C2—82no—
259C2—5842no—
260C2—5842no—
261C2—1462no—
262C2#1798915511yescharacteristic
263C2C2×D8×D7311yescharacteristic
264C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#486×C73C2
socleC22×C73C22×D4
hypercenter#486D73
hypocenterC73#3205
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #17989138C2semidirect
2. #127×D73C2semidirect
3. #17988964C2semidirect
4. #17988963C2semidirect
5. #17988935C2semidirect
6. #17988781C2semidirect
7. #17988722C2semidirect
8. #17988638C2semidirect
9. #486×C73C2semidirect
14. C2×D584C22semidirect
15. C2×#11924013C22semidirect
17. #14556588C22semidirect
25. #14556553C22semidirect
27. #14556520C22semidirect
28. #14556511C22semidirect
30. C4×#10596831C22semidirect
31. C4⋊Q8×C73C22semidirect
33. #102×C73C22semidirect
34. C4×C8×C73C22semidirect
101. C4×D73D8semidirect
133. C73#3205semidirect
139. #486D73semidirect
149. C4⋊Q8C2×D73semidirect
164. #102C2×D73semidirect
167. C4×C8C2×D73semidirect