Finite Group Databasebeta

← #22621530

Subgroups — #22621530

Order 9344.

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

normal subgroups only

This group has 546 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
1C2×#14556618C212yesmaximal, complemented
2#17989240C211yesmaximal, characteristic, complemented
3#17989222C211yesmaximal, characteristic, complemented
4#17988830C212yesmaximal, complemented
5#17988789C211yesmaximal, characteristic, complemented
6#17988779C211yesmaximal, characteristic, complemented
7#17988736C212yesmaximal, complemented
8#17988731C212yesmaximal, complemented
9C4×D584C211yesmaximal, characteristic, complemented
10#17988666C211yesmaximal, characteristic, complemented
11#492×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2212yescomplemented
13C2×D4×D73—21no—
14C2×D4×D73C2212yes—
15#14556618—28no—
16C2×#11924015C2212yes—
17C2×D584C2211yescharacteristic
18C2×#11924013C2212yescomplemented
19C2×#11924011C2212yescomplemented
20#14556576—22no—
21#14556567C2212yescomplemented
22#14556566—21no—
23#14556562—21no—
24#14556562C2212yes—
25#14556559—22no—
26C4×D292C2211yescharacteristic
27C4×D292C2211yescharacteristic
28C4×D292C2211yescharacteristic, complemented
29C4⋊C4×D73—21no—
30#14556525C2211yescharacteristic, complemented
31C4⋊#10596831C2211yescharacteristic, complemented
32#14556515C2212yescomplemented
33#14556513C2211yescharacteristic
34#14556513C2211yescharacteristic, complemented
35#14556512C2212yescomplemented
36#14556503C2212yescomplemented
37C2×SD16×C73C2212yescomplemented
38C2×SD16×C73C2212yescomplemented
39C4⋊Q8×C73C2211yescharacteristic, complemented
40#127×C73C2211yescharacteristic
41C4×C8×C73C2211yescharacteristic, complemented
42C23×D73—22no—
43#11924029—24no—
44#11924029—42no—
45C2×D292—22no—
46C2×D292D411yescharacteristic
47C2×D292C2311yescharacteristic
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—22no—
50C2×C22⋊D73—22no—
51D4×D73—24no—
52D4×D73—42no—
53D4×D73—44no—
54C2×C4×D73—21no—
55C2×C4×D73—21no—
56C2×C4×D73—22no—
57C2×C4×D73C2312yes—
58#11924015—24no—
59D584D414yescomplemented
60#11924013—24no—
61#11924011—24no—
62C2×#10596831C2312yes—
63C4⋊Dic73D411yescharacteristic
64C4⋊Dic73C2311yescharacteristic
65C4⋊Dic73C2311yescharacteristic
66#11924007—22no—
67C22⋊Dic73—22no—
68#11924005—22no—
69#11924005—21no—
70#11924005—21no—
71#11924005D412yes—
72C2×Q8×C73C2312yes—
73C2×D4×C73—21no—
74C2×D4×C73—21no—
75C2×D4×C73C2312yes—
76SD16×C73—24no—
77SD16×C73—42no—
78C2×C8×C73C2311yescharacteristic
79C2×C8×C73C2311yescharacteristic
80C4⋊C4×C73—21no—
81C4⋊C4×C73—21no—
82C42×C73C2311yescharacteristic
83C23×C73—22no—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73—44no—
87C22×D73—44no—
88C22×D73—82no—
89C22×D73C2×D412yes—
90Q8×C73—22no—
91Q8×C73—22no—
92D4×C73—22no—
93D4×C73—22no—
94D4×C73—42no—
95D4×C73—81no—
96C2×C4×C73—22no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2411yescharacteristic
100C22⋊D73—44no—
101C22⋊D73—44no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73C2×D412yes—
105D292—22no—
106D292—21no—
107D292—21no—
108D292—44no—
109D292C2×D412yes—
110D292C2×D412yescomplemented
111C4×D73—22no—
112C4×D73—22no—
113C4×D73—44no—
114C4×D73—42no—
115C4×D73—42no—
116C8×C73—21no—
117C8×C73C2×D412yescomplemented
118#10596831—22no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73C22×D411yescharacteristic
123C2×D73—22no—
124C2×D73—22no—
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—41no—
129C2×D73—41no—
130C2×D73—41no—
131C2×D73—41no—
132C2×D73—88no—
133C4×C73—21no—
134C4×C73—42no—
135C4×C73AGL(1,ℤ/8)12yescomplemented
136C4×C73C22×D411yescharacteristic
137C4×C73H(5,𝔽2)11yescharacteristic
138Dic73—22no—
139Dic73—41no—
140Dic73—41no—
141C2×C73—82no—
142C2×C73D4211yescharacteristic
143C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C73#57711yescharacteristic
145D73—42no—
146D73—42no—
147D73—42no—
148#3272—731nomaximal, Sylow
149C73#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—732no—
151#547—731no—
152D42—731no—
153#492D7311yescharacteristic, complemented
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—732no—
163C22×D4—1461no—
164AGL(1,ℤ/8)—1468no—
165C2×SD16—732no—
166C2×SD16C2×D7312yescomplemented
167C2×SD16C2×D7312yescomplemented
168C2×D8—732no—
169C2×D8—731no—
170C2×M16—732no—
171C4⋊Q8C2×D7311yescharacteristic, complemented
172#127C2×D7311yescharacteristic
173#123—1462no—
174C22⋊Q8—732no—
175#121—732no—
176#121—1461no—
177#121—1461no—
178#120—1462no—
179C4×D4—731no—
180C4×D4—731no—
181C4×D4—731no—
182C2×C4⋊C4—1461no—
183#107—731no—
184C4⋊C8—731no—
185#103—732no—
186#102—732no—
187#102—731no—
188#102—731no—
189C22⋊C8—732no—
190C4×C8C2×D7311yescharacteristic, complemented
191C24—1462no—
192#41—2922no—
193#41—1464no—
194C2×Q8C22×D7312yes—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—2924no—
198C2×D4—2922no—
199C2×D4—731no—
200C2×D4—731no—
201C2×D4—731no—
202C2×D4—1462no—
203C2×D4—1462no—
204C2×D4—1464no—
205C2×D4—1462no—
206C2×D4C22×D7312yes—
207C22×C4—732no—
208C22×C4—1462no—
209C22×C4—1461no—
210C22×C4—1461no—
211SD16—24no—
212SD16—42no—
213SD16—1464no—
214D8—734no—
215D8—1464no—
216M16—1464no—
217C2×C8—732no—
218C2×C8C22×D7311yescharacteristic
219C2×C8C22×D7311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—731no—
223C4⋊C4—731no—
224C4⋊C4—731no—
225C4⋊C4—1462no—
226C22⋊C4—732no—
227C22⋊C4—1462no—
228C22⋊C4—1462no—
229C22⋊C4—1461no—
230C22⋊C4—1461no—
231C42C22×D7311yescharacteristic
232C23—22no—
233C23—2924no—
234C23—2924no—
235C23—5842no—
236C23—732no—
237C23—1461no—
238C23—1461no—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—81no—
245D4—2924no—
246D4—2924no—
247D4—2924no—
248D4—732no—
249D4—732no—
250D4—1462no—
251D4—1461no—
252D4—1461no—
253C2×C4—22no—
254C2×C4—2924no—
255C2×C4—2922no—
256C2×C4—2922no—
257C2×C4—732no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4—1462no—
262C2×C4D4×D7311yescharacteristic
263C2×C4D4×D7311yescharacteristic
264C2×C4C23×D7311yescharacteristic
265C8—21no—
266C8—1462no—
267C8D4×D7312yescomplemented
268C22—42no—
269C22—42no—
270C22—42no—
271C22—2921no—
272C22—2921no—
273C22—2921no—
274C22—2921no—
275C22—5848no—
276C22—1462no—
277C22—1462no—
278C22—1462no—
279C22—1462no—
280C22—1462no—
281C22C2×D4×D7311yescharacteristic
282C4—21no—
283C4—42no—
284C4—2921no—
285C4—2921no—
286C4—1462no—
287C4#1455661812yescomplemented
288C4C2×D4×D7311yescharacteristic
289C4#1455663611yescharacteristic
290C2—82no—
291C2—2922no—
292C2—2922no—
293C2—2922no—
294C2#1798922211yescharacteristic
295C2C2×#1455661811yescharacteristic
296C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#492×C73C2
socleC22×C73C22×D4
hypercenter#492D73
hypocenterC73#3272
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. #17989240C2semidirect
3. #17989222C2semidirect
4. #17988830C2semidirect
5. #17988789C2semidirect
6. #17988779C2semidirect
7. #17988736C2semidirect
8. #17988731C2semidirect
9. C4×D584C2semidirect
10. #17988666C2semidirect
11. #492×C73C2semidirect
12. C2×#11924029C22semidirect
18. C2×#11924013C22semidirect
19. C2×#11924011C22semidirect
21. #14556567C22semidirect
28. C4×D292C22semidirect
30. #14556525C22semidirect
31. C4⋊#10596831C22semidirect
32. #14556515C22semidirect
34. #14556513C22semidirect
35. #14556512C22semidirect
36. #14556503C22semidirect
37. C2×SD16×C73C22semidirect
38. C2×SD16×C73C22semidirect
39. C4⋊Q8×C73C22semidirect
41. C4×C8×C73C22semidirect
59. D584D4semidirect
110. D292C2×D4semidirect
117. C8×C73C2×D4semidirect
135. C4×C73AGL(1,ℤ/8)semidirect
149. C73#3272semidirect
153. #492D73semidirect
166. C2×SD16C2×D73semidirect
167. C2×SD16C2×D73semidirect
171. C4⋊Q8C2×D73semidirect
190. C4×C8C2×D73semidirect
267. C8D4×D73semidirect
287. C4#14556618semidirect