Finite Group Databasebeta

← #22621527

Subgroups — #22621527

Order 9344.

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

normal subgroups only

This group has 546 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#17989242C211yesmaximal, characteristic, complemented
3#17988959C211yesmaximal, characteristic, complemented
4#17988831C212yesmaximal, complemented
5#17988792C211yesmaximal, characteristic, complemented
6#17988779C211yesmaximal, characteristic, complemented
7#17988738C212yesmaximal, complemented
8#17988730C212yesmaximal, complemented
9C4×#11924013C211yesmaximal, characteristic, complemented
10#17988665C211yesmaximal, characteristic, complemented
11D42×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2212yescomplemented
13#14556617—28no—
14C2×#11924016C2212yes—
15C2×#11924016C2212yescomplemented
16C2×#11924016C2212yescomplemented
17C2×#11924013C2211yescharacteristic
18C2×#11924013C2212yescomplemented
19C2×#11924012C2212yescomplemented
20#14556591C2211yescharacteristic, complemented
21#14556573—22no—
22#14556570C2212yescomplemented
23#14556562—21no—
24C4×D292C2211yescharacteristic, complemented
25C4⋊C4×D73—21no—
26#14556524C2211yescharacteristic, complemented
27C4⋊#10596831C2211yescharacteristic, complemented
28#14556514C2212yescomplemented
29#14556512C2211yescharacteristic
30#14556512C2212yescomplemented
31#14556511C2211yescharacteristic, complemented
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×Dic146C2312yes—
45C2×D292C2311yescharacteristic
46C2×C22⋊D73—22no—
47C2×C4×D73—21no—
48C2×C4×D73—22no—
49#11924016—24no—
50#11924016—24no—
51#11924016—42no—
52#11924013—24no—
53#11924013D414yescomplemented
54#11924012—24no—
55C2×#10596831C2311yescharacteristic
56C2×#10596831C2312yes—
57C2×#10596831C2311yescharacteristic
58C4⋊Dic73—21no—
59C4⋊Dic73—21no—
60C4⋊Dic73C2311yescharacteristic
61#11924007—22no—
62C22⋊Dic73—22no—
63#11924005—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—21no—
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—
108C2×Dic73—21no—
109C2×Dic73—22no—
110D292—21no—
111D292C2×D412yescomplemented
112C4×D73—44no—
113C4×D73—42no—
114Dic146—22no—
115Dic146—22no—
116#10596831—22no—
117#10596831—21no—
118#10596831C2×D412yescomplemented
119C22×C73—22no—
120C22×C73—22no—
121C22×C73—22no—
122C22×C73—22no—
123C22×C73—41no—
124C22×C73—41no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—88no—
129C22×C73C22×D411yescharacteristic
130C2×D73—22no—
131C2×D73—41no—
132C2×D73—41no—
133C4×C73—22no—
134C4×C73—21no—
135C4×C73—41no—
136C4×C73AGL(1,ℤ/8)12yescomplemented
137C4×C73C22×D411yescharacteristic
138C4×C73H(5,𝔽2)11yescharacteristic
139Dic73—42no—
140Dic73—41no—
141C2×C73—42no—
142C2×C73—42no—
143C2×C73—82no—
144C2×C73D4211yescharacteristic
145C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C73#57711yescharacteristic
147D73—42no—
148#3272—731nomaximal, Sylow
149C73#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—732no—
151#547—731no—
152D42D7311yescharacteristic, complemented
153#492—731no—
154#468—732no—
155#461—731no—
156#459—731no—
157#450—732no—
158#449—732no—
159C4×D8—731no—
160#436—731no—
161C2×#41—732no—
162C22×D4—21no—
163C22×D4C2×D7312yes—
164AGL(1,ℤ/8)—1468no—
165C2×SD16—732no—
166C2×SD16—732no—
167C2×SD16—732no—
168C2×D8—731no—
169C2×D8—732no—
170C2×M16—732no—
171C4⋊Q8—731no—
172#127C2×D7311yescharacteristic
173#123—1462no—
174C22⋊Q8—732no—
175#121—21no—
176#121—1461no—
177#121C2×D7312yes—
178#120—22no—
179C4×D4—731no—
180C4×D4C2×D7311yescharacteristic
181C4×D4C2×D7311yescharacteristic
182C2×C4⋊C4—1461no—
183#107—731no—
184C4⋊C8—731no—
185#103—732no—
186#102—731no—
187#102—732no—
188#102—731no—
189C22⋊C8—732no—
190C4×C8—731no—
191C24—22no—
192#41—2922no—
193#41—1464no—
194C2×Q8—732no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—731no—
203C2×D4—1462no—
204C2×D4C22⋊D7311yescharacteristic
205C2×D4C22×D7312yes—
206C2×D4C22×D7311yescharacteristic
207C22×C4—21no—
208C22×C4—1461no—
209C22×C4—1462no—
210C22×C4C22×D7312yes—
211SD16—2922no—
212SD16—1464no—
213SD16—1464no—
214D8—734no—
215D8—1464no—
216M16—1464no—
217C2×C8—731no—
218C2×C8—731no—
219C2×C8—732no—
220C4⋊C4—731no—
221C4⋊C4—1462no—
222C4⋊C4—1461no—
223C4⋊C4—1461no—
224C4⋊C4C22⋊D7311yescharacteristic
225C4⋊C4C22×D7311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—1462no—
229C22⋊C4—1461no—
230C22⋊C4C22⋊D7312yes—
231C42C22×D7311yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—1461no—
238C23C2×C22⋊D7312yes—
239Q8—1462no—
240Q8—1462no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—2924no—
250D4—732no—
251D4—1461no—
252D4D4×D7312yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—2924no—
258C2×C4—2922no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4C2×C22⋊D7311yescharacteristic
262C2×C4C2×C22⋊D7312yes—
263C2×C4C2×C22⋊D7311yescharacteristic
264C2×C4C23×D7311yescharacteristic
265C8—732no—
266C8—1462no—
267C8—1461no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—2921no—
279C22—2921no—
280C22—1462no—
281C22C22×C22⋊D7311yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—2922no—
286C4—2921no—
287C4#1455661712yescomplemented
288C4C2×D4×D7311yescharacteristic
289C4#1455663611yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—2922no—
294C2D4×C22⋊D7311yescharacteristic
295C2C2×#1455661711yescharacteristic
296C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingD42×C73C2
socleC22×C73C22×D4
hypercenterD42D73
hypocenterC73#3272
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. #17989242C2semidirect
3. #17988959C2semidirect
4. #17988831C2semidirect
5. #17988792C2semidirect
6. #17988779C2semidirect
7. #17988738C2semidirect
8. #17988730C2semidirect
9. C4×#11924013C2semidirect
10. #17988665C2semidirect
11. D42×C73C2semidirect
12. C2×#11924028C22semidirect
15. C2×#11924016C22semidirect
16. C2×#11924016C22semidirect
18. C2×#11924013C22semidirect
19. C2×#11924012C22semidirect
20. #14556591C22semidirect
22. #14556570C22semidirect
24. C4×D292C22semidirect
26. #14556524C22semidirect
27. C4⋊#10596831C22semidirect
28. #14556514C22semidirect
30. #14556512C22semidirect
31. #14556511C22semidirect
32. C22⋊#10596831C22semidirect
33. C4×#10596831C22semidirect
53. #11924013D4semidirect
111. D292C2×D4semidirect
118. #10596831C2×D4semidirect
136. C4×C73AGL(1,ℤ/8)semidirect
149. C73#3272semidirect
152. D42D73semidirect
287. C4#14556617semidirect