Finite Group Databasebeta

← #22621547

Subgroups — #22621547

Order 9344.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556617C212yesmaximal, complemented
2#17989258C211yesmaximal, characteristic, complemented
3#17988963C211yesmaximal, characteristic, complemented
4#17988838C212yesmaximal, complemented
5#17988784C211yesmaximal, characteristic, complemented
6#17988782C211yesmaximal, characteristic, complemented
7#17988730C212yesmaximal, complemented
8#17988721C212yesmaximal, complemented
9C4×#11924016C211yesmaximal, characteristic, complemented
10#17988665C211yesmaximal, characteristic, complemented
11D42×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2212yescomplemented
13#14556617—28no—
14C2×#11924016C2211yescharacteristic
15C2×#11924016C2212yescomplemented
16C2×#11924013C2212yes—
17C2×#11924013C2212yescomplemented
18C2×#11924013C2212yescomplemented
19C2×#11924012C2212yescomplemented
20#14556588C2211yescharacteristic, complemented
21#14556587—21no—
22#14556565C2212yescomplemented
23#14556564—22no—
24C4×Dic146C2211yescharacteristic, complemented
25#14556553—21no—
26#14556522C2211yescharacteristic, complemented
27C4⋊#10596831C2211yescharacteristic, complemented
28#14556514C2211yescharacteristic, complemented
29#14556512C2211yescharacteristic
30#14556512C2212yescomplemented
31#14556511C2212yescomplemented
32C22⋊#10596831C2212yescomplemented
33C4×#10596831C2211yescharacteristic, complemented
34C22×D4×C73—21no—
35C22×D4×C73C2212yes—
36#127×C73C2211yescharacteristic
37#121×C73—21no—
38#121×C73C2212yes—
39#120×C73—22no—
40C4×D4×C73C2211yescharacteristic
41C4×D4×C73C2211yescharacteristic
42#11924028—24no—
43#11924028—42no—
44C2×Dic146C2311yescharacteristic
45C2×D292—21no—
46C2×D292—21no—
47C2×D292C2312yes—
48C2×C22⋊D73—22no—
49C2×C22⋊D73—22no—
50C2×C4×D73—22no—
51#11924016—24no—
52#11924016D414yescomplemented
53#11924013—24no—
54#11924013—24no—
55#11924013—42no—
56#11924012—24no—
57C2×#10596831C2311yescharacteristic
58C2×#10596831C2312yes—
59C2×#10596831C2311yescharacteristic
60C4⋊Dic73C2311yescharacteristic
61#11924007—21no—
62#11924005—22no—
63C4×Dic73—21no—
64C24×C73—22no—
65C2×D4×C73—24no—
66C2×D4×C73—22no—
67C2×D4×C73—22no—
68C2×D4×C73—21no—
69C2×D4×C73—21no—
70C2×D4×C73—42no—
71C2×D4×C73—44no—
72C2×D4×C73D411yescharacteristic
73C2×D4×C73C2312yes—
74C2×D4×C73C2311yescharacteristic
75C22×C4×C73—21no—
76C22×C4×C73C2312yes—
77C4⋊C4×C73D411yescharacteristic
78C4⋊C4×C73C2311yescharacteristic
79C22⋊C4×C73—21no—
80C22⋊C4×C73—22no—
81C22⋊C4×C73D412yes—
82C42×C73C2311yescharacteristic
83C23×C73—21no—
84C23×C73—22no—
85C23×C73—44no—
86C23×C73—44no—
87C23×C73—82no—
88C23×C73C2×D412yes—
89C22×D73—22no—
90D4×C73—22no—
91D4×C73—22no—
92D4×C73—21no—
93D4×C73—22no—
94D4×C73—44no—
95D4×C73—44no—
96D4×C73—42no—
97D4×C73—81no—
98D4×C73C2×D412yes—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73—42no—
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2×D412yes—
105C2×C4×C73C2×D411yescharacteristic
106C2×C4×C73C2411yescharacteristic
107C22⋊D73—44no—
108C22⋊D73—82no—
109C2×Dic73—21no—
110C2×Dic73—21no—
111D292—22no—
112D292—22no—
113D292—42no—
114D292—81no—
115C4×D73—44no—
116Dic146—21no—
117Dic146C2×D412yescomplemented
118#10596831—22no—
119#10596831—21no—
120#10596831C2×D412yescomplemented
121C22×C73—22no—
122C22×C73—22no—
123C22×C73—22no—
124C22×C73—22no—
125C22×C73—41no—
126C22×C73—41no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73—88no—
131C22×C73C22×D411yescharacteristic
132C2×D73—42no—
133C2×D73—42no—
134C2×D73—42no—
135C4×C73—22no—
136C4×C73—21no—
137C4×C73—41no—
138C4×C73AGL(1,ℤ/8)12yescomplemented
139C4×C73C22×D411yescharacteristic
140C4×C73H(5,𝔽2)11yescharacteristic
141Dic73—22no—
142Dic73—41no—
143C2×C73—42no—
144C2×C73—42no—
145C2×C73—82no—
146C2×C73D4211yescharacteristic
147C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C73#57611yescharacteristic
149D73—82no—
150#3274—731nomaximal, Sylow
151C73#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—732no—
153#550—731no—
154D42D7311yescharacteristic, complemented
155#493—731no—
156#469—732no—
157#460—731no—
158#459—731no—
159#449—732no—
160#447—732no—
161C4×SD16—731no—
162#436—731no—
163C2×#41—732no—
164C22×D4—21no—
165C22×D4C2×D7312yes—
166AGL(1,ℤ/8)—1468no—
167C2×SD16—731no—
168C2×SD16—732no—
169C2×D8—732no—
170C2×D8—732no—
171C2×D8—732no—
172C2×M16—732no—
173#127—731no—
174#127—1461no—
175#127C2×D7311yescharacteristic
176#121—21no—
177#121—732no—
178#121—1462no—
179#121C2×D7312yes—
180#120—22no—
181C4×Q8—731no—
182C4×D4—1461no—
183C4×D4C2×D7311yescharacteristic
184C4×D4C2×D7311yescharacteristic
185#106—731no—
186C4⋊C8—731no—
187#103—731no—
188#102—731no—
189#102—732no—
190#102—732no—
191C22⋊C8—732no—
192C4×C8—731no—
193C24—22no—
194#41—2922no—
195#41—1464no—
196C2×Q8—731no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—42no—
203C2×D4—44no—
204C2×D4—732no—
205C2×D4—1462no—
206C2×D4—1462no—
207C2×D4—1461no—
208C2×D4—1461no—
209C2×D4C22⋊D7311yescharacteristic
210C2×D4C22×D7312yes—
211C2×D4C22×D7311yescharacteristic
212C22×C4—21no—
213C22×C4—1462no—
214C22×C4C22×D7312yes—
215SD16—734no—
216SD16—1464no—
217D8—2922no—
218D8—1464no—
219D8—1464no—
220M16—1464no—
221C2×C8—731no—
222C2×C8—731no—
223C2×C8—732no—
224C4⋊C4—731no—
225C4⋊C4—1461no—
226C4⋊C4C22⋊D7311yescharacteristic
227C4⋊C4C22×D7311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—1462no—
231C22⋊C4C22⋊D7312yes—
232C42—1461no—
233C42C22×D7311yescharacteristic
234C23—21no—
235C23—22no—
236C23—44no—
237C23—44no—
238C23—82no—
239C23—1462no—
240C23C2×C22⋊D7312yes—
241Q8—732no—
242Q8—1461no—
243D4—22no—
244D4—22no—
245D4—21no—
246D4—22no—
247D4—44no—
248D4—44no—
249D4—42no—
250D4—81no—
251D4—2924no—
252D4—2922no—
253D4—5841no—
254D4—5842no—
255D4—1462no—
256D4—1462no—
257D4D4×D7312yes—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—2924no—
263C2×C4—1461no—
264C2×C4—1461no—
265C2×C4C2×C22⋊D7311yescharacteristic
266C2×C4C2×C22⋊D7312yes—
267C2×C4C2×C22⋊D7311yescharacteristic
268C2×C4C23×D7311yescharacteristic
269C8—732no—
270C8—1462no—
271C8—1461no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—88no—
282C22—2922no—
283C22—2922no—
284C22—2922no—
285C22C22×C22⋊D7311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—2921no—
290C4—1462no—
291C4#1455661712yescomplemented
292C4C2×D4×D7311yescharacteristic
293C4#1455663611yescharacteristic
294C2—42no—
295C2—42no—
296C2—82no—
297C2—5842no—
298C2D4×C22⋊D7311yescharacteristic
299C2C2×#1455661711yescharacteristic
300C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingD42×C73C2
socleC22×C73C22×D4
hypercenterD42D73
hypocenterC73#3274
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14556617C2semidirect
2. #17989258C2semidirect
3. #17988963C2semidirect
4. #17988838C2semidirect
5. #17988784C2semidirect
6. #17988782C2semidirect
7. #17988730C2semidirect
8. #17988721C2semidirect
9. C4×#11924016C2semidirect
10. #17988665C2semidirect
11. D42×C73C2semidirect
12. C2×#11924028C22semidirect
15. C2×#11924016C22semidirect
17. C2×#11924013C22semidirect
18. C2×#11924013C22semidirect
19. C2×#11924012C22semidirect
20. #14556588C22semidirect
22. #14556565C22semidirect
24. C4×Dic146C22semidirect
26. #14556522C22semidirect
27. C4⋊#10596831C22semidirect
28. #14556514C22semidirect
30. #14556512C22semidirect
31. #14556511C22semidirect
32. C22⋊#10596831C22semidirect
33. C4×#10596831C22semidirect
52. #11924016D4semidirect
117. Dic146C2×D4semidirect
120. #10596831C2×D4semidirect
138. C4×C73AGL(1,ℤ/8)semidirect
151. C73#3274semidirect
154. D42D73semidirect
291. C4#14556617semidirect