Finite Group Databasebeta

← #22620873

Subgroups — #22620873

Order 9344.

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

normal subgroups only

This group has 488 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#17989142C211yesmaximal, characteristic, complemented
2#127×D73C211yesmaximal, characteristic
3#17988960C211yesmaximal, characteristic, complemented
4#17988959C211yesmaximal, characteristic, complemented
5#17988935C211yesmaximal, characteristic, complemented
6#17988786C214yesmaximal, complemented
7#17988739C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#486×C73C211yesmaximal, characteristic, complemented
10C2×D4×D73—21no—
11C2×D4×D73—21no—
12C2×D4×D73C2212yes—
13C2×#11924017C2214yescomplemented
14C2×#11924016C2214yescomplemented
15#14556591C2211yescharacteristic, complemented
16#14556588C2211yescharacteristic
17#14556587—21no—
18#14556587—21no—
19#14556587C2212yes—
20#14556582—21no—
21#14556571C2212yes—
22#14556567—21no—
23Q8×Dic73—21no—
24#14556556C2212yescomplemented
25#14556549—21no—
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—
36C2×Dic146C2312yes—
37C2×D292—21no—
38C2×D292—21no—
39C2×D292C2312yes—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73—22no—
43D4×D73—44no—
44D4×D73—44no—
45D4×D73—44no—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49#11924017—44no—
50#11924016—44no—
51C2×#10596831C2312yes—
52C4⋊Dic73—21no—
53C4⋊Dic73—21no—
54C4⋊Dic73—22no—
55#11924007—22no—
56#11924005—22no—
57C4×Dic73—22no—
58C4×Dic73D411yescharacteristic
59C4×Dic73D411yescharacteristic
60C4×Dic73C2311yescharacteristic
61C2×Q8×C73—21no—
62C2×D4×C73—21no—
63C2×D4×C73—21no—
64C2×D4×C73C2312yes—
65C2×C8×C73C2312yes—
66C4⋊C4×C73—21no—
67C4⋊C4×C73C2312yes—
68C42×C73C2311yescharacteristic
69C23×C73—22no—
70C22×D73—22no—
71C22×D73—44no—
72C22×D73—44no—
73C22×D73—44no—
74C22×D73C2×D411yescharacteristic
75Q8×C73—42no—
76D4×C73—24no—
77D4×C73—42no—
78D4×C73—42no—
79C2×C4×C73—22no—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2411yescharacteristic
83C22⋊D73—44no—
84C22⋊D73—44no—
85C22⋊D73—44no—
86C2×Dic73—22no—
87C2×Dic73C2×D411yescharacteristic
88C2×Dic73C2×D411yescharacteristic
89C2×Dic73C2×D411yescharacteristic
90D292—24no—
91D292—42no—
92D292—42no—
93C4×D73—22no—
94C4×D73—22no—
95C4×D73SD1614yescomplemented
96Dic146—24no—
97C8×C73—22no—
98#10596831—22no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73C22×D411yescharacteristic
103C2×D73—21no—
104C2×D73—21no—
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—88no—
109C2×D73C2×SD1612yes—
110C4×C73—42no—
111C4×C73C2×SD1612yes—
112C4×C73AGL(1,ℤ/8)12yes—
113C4×C73H(5,𝔽2)12yes—
114Dic73—21no—
115Dic73—21no—
116Dic73—42no—
117Dic73C2×SD1612yes—
118C2×C73—82no—
119C2×C73#53511yescharacteristic
120C2×C73C22×SD1611yescharacteristic
121C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
122D73—22no—
123D73—82no—
124#3208—731nomaximal, Sylow
125C73#320811yescharacteristic, complemented, Sylow
126#533—731no—
127C2×#127—731no—
128#492—731no—
129#492—731no—
130#486—731no—
131#486D7311yescharacteristic, complemented
132#460—734no—
133#450—734no—
134#431—731no—
135C22×D4—732no—
136C22×D4—1461no—
137C22×D4—1461no—
138C2×SD16—734no—
139C2×SD16—734no—
140C4⋊Q8—731no—
141C4⋊Q8C2×D7311yescharacteristic, complemented
142#127—732no—
143#127—731no—
144#127—1461no—
145#127—1461no—
146#127C2×D7311yescharacteristic
147#125—1461no—
148C22⋊Q8—732no—
149C22⋊Q8—1461no—
150C4×Q8—732no—
151C4×Q8—1461no—
152#117—1461no—
153C2×C42—731no—
154C4⋊C8—732no—
155#102—734no—
156#102C2×D7314yescomplemented
157C22⋊C8—732no—
158C4×C8—731no—
159C4×C8C2×D7311yescharacteristic, complemented
160C24—1462no—
161C2×Q8—21no—
162C2×Q8—732no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—2924no—
166C2×D4—2924no—
167C2×D4—2924no—
168C2×D4—732no—
169C2×D4—1462no—
170C2×D4—1462no—
171C2×D4—1462no—
172C2×D4—1461no—
173C2×D4—1461no—
174C2×D4C22×D7312yes—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—731no—
178SD16—2924no—
179SD16—2924no—
180C2×C8—732no—
181C2×C8C22×D7312yes—
182C4⋊C4—21no—
183C4⋊C4—1462no—
184C4⋊C4—1462no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C4⋊C4C22×D7312yes—
188C22⋊C4—1462no—
189C42—731no—
190C42—731no—
191C42—731no—
192C42—1462no—
193C42C22×D7311yescharacteristic
194C23—22no—
195C23—2924no—
196C23—2924no—
197C23—2924no—
198C23—731no—
199C23—1462no—
200Q8—42no—
201Q8—1464no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—2924no—
206D4—2924no—
207D4—2924no—
208D4—2922no—
209D4—2922no—
210D4—1464no—
211C2×C4—22no—
212C2×C4—731no—
213C2×C4—734no—
214C2×C4—731no—
215C2×C4—731no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4D4×D7311yescharacteristic
220C2×C4D4×D7311yescharacteristic
221C2×C4C23×D7311yescharacteristic
222C8—22no—
223C8—1462no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—2922no—
228C22—2922no—
229C22—2922no—
230C22—5848no—
231C22—732no—
232C22—1461no—
233C22—1461no—
234C22C2×D4×D7311yescharacteristic
235C4—42no—
236C4—2922no—
237C4—732no—
238C4—1461no—
239C4—1461no—
240C4SD16×D7312yes—
241C4#1455661512yes—
242C4#1455663712yes—
243C2—82no—
244C2—5842no—
245C2—1462no—
246C2#1798915511yescharacteristic
247C2C2×SD16×D7311yescharacteristic
248C2C2×#1455661511yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#486×C73C2
socleC22×C73C22×D4
hypercenter#486D73
hypocenterC73#3208
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. #17989142C2semidirect
3. #17988960C2semidirect
4. #17988959C2semidirect
5. #17988935C2semidirect
6. #17988786C2semidirect
7. #17988739C2semidirect
8. #17988638C2semidirect
9. #486×C73C2semidirect
13. C2×#11924017C22semidirect
14. C2×#11924016C22semidirect
15. #14556591C22semidirect
24. #14556556C22semidirect
27. #14556520C22semidirect
28. #14556511C22semidirect
30. C4×#10596831C22semidirect
31. C4⋊Q8×C73C22semidirect
33. #102×C73C22semidirect
34. C4×C8×C73C22semidirect
95. C4×D73SD16semidirect
125. C73#3208semidirect
131. #486D73semidirect
141. C4⋊Q8C2×D73semidirect
156. #102C2×D73semidirect
159. C4×C8C2×D73semidirect